%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Roger A. Horn and Charles R. Johnson and
%%%                        Nelson H. F. Beebe",
%%%     version         = "1.06",
%%%     date            = "13 May 2024",
%%%     time            = "08:52:57 MST",
%%%     filename        = "matrix-analysis-2ed.bib",
%%%     address-1       = "University of Utah
%%%                        Department of Mathematics
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     address-2       = "Charles R. Johnson
%%%                        Department of Mathematics
%%%                        The College of William & Mary
%%%                        Williamsburg, VA 23187-8795
%%%                        USA",
%%%     address-3       = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone-2     = "+1 757 221 2014",
%%%     telephone-3     = "+1 801 581 5254",
%%%     FAX-1           = "+1 801 581 4148",
%%%     FAX-3           = "+1 801 581 4148",
%%%     URL-2           = "http://www.wm.edu/as/mathematics/faculty/directory/johnson_c.php",
%%%     URL-3           = "https://www.math.utah.edu/~beebe",
%%%     checksum        = "15741 13791 72167 678503",
%%%     email-1         = "rhorn at math.utah.edu",
%%%     email-2         = "crjohnso at math.wm.edu",
%%%     email-3         = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; BibTeX; linear algebra; matrix
%%%                        analysis; numerical analysis",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of books that are
%%%                        referenced in the second edition of Roger
%%%                        Horn and Charles Johnson's 2012 book ``Matrix
%%%                        Analysis''.  It also includes additional
%%%                        entries for earlier and later editions of the
%%%                        referenced books, entries for books with
%%%                        similar titles to cited works that are likely
%%%                        to be closely related, and entries for reviews
%%%                        of ``Matrix Analysis''.
%%%
%%%                        At version 1.06, the year coverage looked like
%%%                        this:
%%%
%%%                             1877 (   1)    1924 (   1)    1971 (   5)
%%%                             1878 (   0)    1925 (   0)    1972 (   5)
%%%                             1879 (   0)    1926 (   0)    1973 (   6)
%%%                             1880 (   0)    1927 (   0)    1974 (   3)
%%%                             1881 (   0)    1928 (   0)    1975 (   4)
%%%                             1882 (   0)    1929 (   0)    1976 (   3)
%%%                             1883 (   0)    1930 (   1)    1977 (   1)
%%%                             1884 (   0)    1931 (   0)    1978 (   3)
%%%                             1885 (   0)    1932 (   1)    1979 (   6)
%%%                             1886 (   0)    1933 (   1)    1980 (   2)
%%%                             1887 (   0)    1934 (   2)    1981 (   3)
%%%                             1888 (   0)    1935 (   0)    1982 (   4)
%%%                             1889 (   0)    1936 (   1)    1983 (   4)
%%%                             1890 (   0)    1937 (   1)    1984 (   2)
%%%                             1891 (   0)    1938 (   0)    1985 (   4)
%%%                             1892 (   0)    1939 (   1)    1986 (   2)
%%%                             1893 (   0)    1940 (   0)    1987 (   4)
%%%                             1894 (   1)    1941 (   0)    1988 (   6)
%%%                             1895 (   0)    1942 (   2)    1989 (   4)
%%%                             1896 (   0)    1943 (   1)    1990 (   6)
%%%                             1897 (   0)    1944 (   0)    1991 (   4)
%%%                             1898 (   0)    1945 (   1)    1992 (   3)
%%%                             1899 (   0)    1946 (   2)    1993 (   2)
%%%                             1900 (   0)    1947 (   0)    1994 (   1)
%%%                             1901 (   0)    1948 (   1)    1995 (   5)
%%%                             1902 (   0)    1949 (   0)    1996 (   4)
%%%                             1903 (   0)    1950 (   3)    1997 (   2)
%%%                             1904 (   0)    1951 (   0)    1998 (   2)
%%%                             1905 (   0)    1952 (   2)    1999 (   0)
%%%                             1906 (   1)    1953 (   2)    2000 (   3)
%%%                             1907 (   0)    1954 (   2)    2001 (   0)
%%%                             1908 (   0)    1955 (   1)    2002 (   3)
%%%                             1909 (   0)    1956 (   1)    2003 (   2)
%%%                             1910 (   0)    1957 (   0)    2004 (   3)
%%%                             1911 (   0)    1958 (   3)    2005 (   5)
%%%                             1912 (   0)    1959 (   6)    2006 (   6)
%%%                             1913 (   0)    1960 (   6)    2007 (   7)
%%%                             1914 (   0)    1961 (   4)    2008 (   2)
%%%                             1915 (   0)    1962 (   3)    2009 (   4)
%%%                             1916 (   0)    1963 (   3)    2010 (   0)
%%%                             1917 (   0)    1964 (   6)    2011 (   5)
%%%                             1918 (   0)    1965 (   2)    2012 (   1)
%%%                             1919 (   0)    1966 (   3)    2013 (   0)
%%%                             1920 (   0)    1967 (   4)    2014 (   0)
%%%                             1921 (   0)    1968 (   5)    2015 (   1)
%%%                             1922 (   0)    1969 (   7)
%%%                             1923 (   0)    1970 (   4)
%%%
%%%                             Article:          2
%%%                             Book:           224
%%%                             TechReport:       2
%%%
%%%                             Total entries:  228
%%%
%%%                        Data for this bibliography have been obtained
%%%                        from many different library catalogs and
%%%                        publisher Web sites.
%%%
%%%                        Numerous errors in the sources noted above
%%%                        have been corrected.  Spelling has been
%%%                        verified with the UNIX spell and GNU ispell
%%%                        programs using the exception dictionary
%%%                        stored in the companion file with extension
%%%                        .sok.
%%%
%%%                        For nearly half the entries,
%%%                        table-of-contents data are supplied from
%%%                        library catalog and publisher resources.
%%%                        Because those data have often been obtained
%%%                        from digital bitmap scans of original pages
%%%                        and further processed by
%%%                        optical-character-recognition (OCR) software,
%%%                        they are frequently in error because of
%%%                        faulty character identification, particularly
%%%                        for accents and mathematical symbols, for
%%%                        subscripts, superscripts, and font changes,
%%%                        and for look-alike characters.  Substantial
%%%                        efforts have been made to find and repair
%%%                        those errors, but some flaws undoubtedly
%%%                        remain.  They will be correctly promptly when
%%%                        the third author is notified of them.
%%%
%%%                        English translations are provided for
%%%                        foreign-language titles, but not for their
%%%                        tables of contents.  Such entries also
%%%                        contain a language key assignment.
%%%
%%%                        BibTeX citation tags are uniformly chosen as
%%%                        name:year:abbrev, where name is the family
%%%                        name of the first author or editor, year is a
%%%                        4-digit number, and abbrev is a 3-letter
%%%                        condensation of important title
%%%                        words. Citation tags were automatically
%%%                        generated by software developed for the
%%%                        BibNet Project.
%%%
%%%                        In this bibliography, entries are sorted by
%%%                        citation label, matching the order used in
%%%                        ``Matrix Analysis'', and grouping together
%%%                        successive editions.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

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 # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi"
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 # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi"
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%%% ====================================================================
%%% Acknowledgement abbreviations:

@String{ack-crj =  "Charles R. Johnson,
                    Department of Mathematics,
                    The College of William \& Mary,
                    Williamsburg, VA 23187-8795, USA,
                    e-mail: \path|[email protected]|"}

@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|[email protected]|,
                            \path|[email protected]|,
                            \path|[email protected]| (Internet),
                    URL: \path|https://www.math.utah.edu/~beebe/|"}

@String{ack-njh =   "Nick Higham,
                    e-mail: \path|[email protected]|"}

@String{ack-rah = "Roger A. Horn,
                   University of Utah,
                   Department of Mathematics,
                   155 S 1400 E RM 233,
                   Salt Lake City, UT 84112-0090, USA,
                   Tel: +1 801 585 6819,
                   FAX: +1 801 581 4148,
                   e-mail: \path|[email protected]| (Internet)"}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and its Applications"}

%%% ====================================================================
%%% Publishers and their addresses:

@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, NY, USA"}

@String{pub-AKADEMIE-VERLAG     = "Akademie-Verlag"}
@String{pub-AKADEMIE-VERLAG:adr = "Berlin, Germany"}

@String{pub-ALLYN-BACON         = "Allyn and Bacon"}
@String{pub-ALLYN-BACON:adr     = "Needham Heights, MA, USA"}

@String{pub-AMS                 = "American Mathematical Society"}
@String{pub-AMS:adr             = "Providence, RI, USA"}

@String{pub-AW                  = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
@String{pub-AW:adr              = "Reading, MA, USA"}

@String{pub-BLACKIE             = "Blackie"}
@String{pub-BLACKIE:adr         = "Glasgow, Scotland"}

@String{pub-BIBLIO-INST         = "Bibliographisches Institut"}
@String{pub-BIBLIO-INST:adr     = "Mannheim, Germany"}

@String{pub-BIRKHAUSER          = "Birkh{\"{a}}user"}
@String{pub-BIRKHAUSER:adr      = "Cambridge, MA, USA; Berlin, Germany; Basel,
                                  Switzerland"}

@String{pub-BIRKHAUSER-BOSTON   = "Birkh{\"a}user Boston Inc."}
@String{pub-BIRKHAUSER-BOSTON:adr = "Cambridge, MA, USA"}

@String{pub-BN                  = "Barnes and Noble"}
@String{pub-BN:adr              = "New York, NY, USA"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-CHAPMAN-HALL-CRC    = "Chapman and Hall/CRC"}
@String{pub-CHAPMAN-HALL-CRC:adr = "Boca Raton, FL, USA"}

@String{pub-CLARENDON           = "Clarendon Press"}
@String{pub-CLARENDON:adr       = "Oxford, UK and New York, NY, USA"}

@String{pub-DEKKER              = "Marcel Dekker, Inc."}
@String{pub-DEKKER:adr          = "New York, NY, USA"}

@String{pub-DOVER               = "Dover"}
@String{pub-DOVER:adr           = "New York, NY, USA"}

@String{pub-ELLIS-HORWOOD       = "Ellis Horwood"}
@String{pub-ELLIS-HORWOOD:adr   = "New York, NY, USA"}

@String{pub-GREENWOOD           = "Greenwood Press"}
@String{pub-GREENWOOD:adr       = "88 Post Road West, Westport, CT 06881, USA"}

@String{pub-GRUYTER             = "Walter de Gruyter"}
@String{pub-GRUYTER:adr         = "New York, NY, USA"}

@String{pub-HALSTED             = "Halsted Press"}
@String{pub-HALSTED:adr         = "New York, USA"}

@String{pub-JOHNS-HOPKINS       = "The Johns Hopkins University Press"}
@String{pub-JOHNS-HOPKINS:adr   = "Baltimore, MD, USA"}

@String{pub-KLUWER              = "Kluwer Academic Publishers Group"}
@String{pub-KLUWER:adr          = "Norwell, MA, USA, and Dordrecht,
                                  The Netherlands"}

@String{pub-LONGMAN             = "Longman Scientific and Technical"}
@String{pub-LONGMAN:adr         = "Harlow, Essex, UK"}

@String{pub-MAA                 = "Mathematical Association of America"}
@String{pub-MAA:adr             = "Washington, DC, USA"}

@String{pub-MACMILLAN           = "Macmillan Publishing Company"}
@String{pub-MACMILLAN:adr       = "New York, NY, USA and London, UK"}

@String{pub-MCGRAW-HILL         = "Mc{\-}Graw-Hill"}
@String{pub-MCGRAW-HILL:adr     = "New York, NY, USA"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PH                  = "Pren{\-}tice-Hall"}
@String{pub-PH:adr              = "Upper Saddle River, NJ 07458, USA"}

@String{pub-PITMAN              = "Pitman Publishing Ltd."}
@String{pub-PITMAN:adr          = "London, UK"}

@String{pub-PLENUM              = "Plenum Press"}
@String{pub-PLENUM:adr          = "New York, NY, USA; London, UK"}

@String{pub-PRINCETON           = "Princeton University Press"}
@String{pub-PRINCETON:adr       = "Princeton, NJ, USA"}

@String{pub-R-E-KRIEGER         = "Robert E. Krieger Publishing Company"}
@String{pub-R-E-KRIEGER:adr     = "Huntington, NY, USA"}

@String{pub-SIAM                = "Society for Industrial and Applied
                                  Mathematics"}
@String{pub-SIAM:adr            = "Philadelphia, PA, USA"}

@String{pub-STANFORD            = "Stanford University Press"}
@String{pub-STANFORD:adr        = "Stanford, CA, USA"}

@String{pub-SV                  = "Springer-Verlag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg, Germany~/
                                    London, UK~/ etc."}

@String{pub-TEUBNER             = "Teubner"}
@String{pub-TEUBNER:adr         = "Stuttgart, Germany; Leipzig, Germany"}

@String{pub-U-NC                = "University of North Carolina Press"}
@String{pub-U-NC:adr            = "Chapel Hill, NC, USA"}

@String{pub-W-H-FREEMAN         = "W. H. Freeman"}
@String{pub-W-H-FREEMAN:adr     = "New York, NY, USA"}

@String{pub-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA"}

@String{pub-WILEY-INTERSCIENCE  = "Wiley-In{\-}ter{\-}sci{\-}ence"}
@String{pub-WILEY-INTERSCIENCE:adr = "New York, NY, USA"}

%%% ====================================================================
%%% Series abbreviations:

@String{ser-LECT-NOTES-MATH     = "Lecture Notes in Mathematics"}

%%% ====================================================================
%%%                          Part 1 (of 2)
%%%
%%%             Books referenced in ``Matrix Analysis''
%%%               (second edition: entry Horn:2012:MA)
%%%
%%% This bibliography includes entries for several other books that are
%%% earlier or later editions, or have almost identical titles (and
%%% thus, are likely to be closely related to the material in ``Matrix
%%% Analysis'').  The reference list in that book records 115 distinct
%%% books.  This bibliography, which may be updated from time to time
%%% with new data, has entries for at least 228 books and reports,
%%% including ALL of those listed in ``Matrix Analysis''.
%%%
%%% Entries for books referenced in ``Matrix Analysis'' are identified
%%% by an acknowledgement value of ack-rah or ack-crj (the first and
%%% second author of this bibliography).  Those with acknowledgement
%%% values of ack-nhfb have been supplied by the third author, who
%%% prepared this bibliography from the book's original raw reference
%%% list, and maintains the BibTeX entries and all of the software that
%%% supports their creation, checking, and validation.
%%%
%%% Bibliography entries, sorted by citation label, with "bibsort",
%%% matching the reference list order in ``Matrix Analysis'', and
%%% grouping successive book editions together:

@Book{Aitken:1939:DM,
  author =       "A. C. (Alexander Craig) Aitken",
  title =        "Determinants and Matrices",
  publisher =    "Oliver and Boyd",
  address =      "Edinburgh, UK",
  pages =        "vii + 135",
  year =         "1939",
  LCCN =         "QA191 .A5",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "University mathematical texts",
  acknowledgement = ack-nhfb,
  author-dates = "1895--",
  remark =       "Errata slip attached to p. [v].",
  subject =      "Determinants; Matrices",
}

@Book{Aitken:1946:DM,
  author =       "A. C. (Alexander Craig) Aitken",
  title =        "Determinants and Matrices",
  publisher =    "Oliver and Boyd",
  address =      "Edinburgh and London, UK",
  edition =      "Fourth",
  pages =        "vii + 143 + 1",
  year =         "1946",
  LCCN =         "QA191 .A5 1946",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1895--",
  subject =      "Determinants; Matrices",
}

@Book{Aitken:1948:DM,
  author =       "A. C. (Alexander Craig) Aitken",
  title =        "Determinants and Matrices",
  publisher =    "Oliver and Boyd",
  address =      "Edinburgh, UK",
  edition =      "Fifth",
  pages =        "vii + 143",
  year =         "1948",
  LCCN =         "QA191 .A5 1948",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "University mathematical texts",
  acknowledgement = ack-nhfb,
  author-dates = "1895--",
  subject =      "Determinants; Matrices",
}

@Book{Aitken:1954:DM,
  author =       "A. C. (Alexander Craig) Aitken",
  title =        "Determinants and Matrices",
  publisher =    "Oliver and Boyd",
  address =      "Edinburgh, UK",
  edition =      "Eighth",
  pages =        "144",
  year =         "1954",
  LCCN =         "QA191 .A5 1954",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "University mathematical texts",
  acknowledgement = ack-nhfb,
  author-dates = "1895--",
  subject =      "Determinants; Matrices",
}

@Book{Aitken:1956:DM,
  author =       "A. C. (Alexander Craig) Aitken",
  title =        "Determinants and Matrices",
  publisher =    "Oliver and Boyd",
  address =      "Edinburgh, UK",
  edition =      "Ninth",
  pages =        "144",
  year =         "1956",
  LCCN =         "QA191 .A5 1956",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "University mathematical texts",
  acknowledgement = ack-nhfb,
  author-dates = "1895--",
  subject =      "Determinants; Matrices",
}

@Book{Aitken:1969:DMG,
  author =       "A. C. (Alexander Craig) Aitken",
  title =        "{Determinanten und Matrizen}. ({German}) [Determinants
                 and Matrices]",
  volume =       "293",
  publisher =    pub-BIBLIO-INST,
  address =      pub-BIBLIO-INST:adr,
  pages =        "142",
  year =         "1969",
  LCCN =         "QA191 .A515",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translation to German by Winfried Nilson of
                 \cite{Aitken:1956:DM}.",
  series =       "B.I.-Hochschultaschenb{\"u}cher",
  acknowledgement = ack-nhfb,
  author-dates = "1895--",
  language =     "German",
  subject =      "Determinants; Matrices",
}

@Book{Aitken:1983:DM,
  author =       "A. C. (Alexander Craig) Aitken",
  title =        "Determinants and Matrices",
  publisher =    pub-GREENWOOD,
  address =      pub-GREENWOOD:adr,
  edition =      "Revised",
  pages =        "vii + 144",
  year =         "1983",
  ISBN =         "0-313-23294-6",
  ISBN-13 =      "978-0-313-23294-7",
  LCCN =         "QA191 .A5 1983",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1895--",
  remark =       "Reprint. Originally published: Edinburgh: Oliver and
                 Boyd, 1946.",
  subject =      "Definitions and fundamental operations of matrices;
                 Definition and properties of determinants; Adjugate and
                 reciprocal matrix: solution of simultaneous equations:
                 rank and linear dependence; Cauchy and Laplace
                 expansions: multiplication theorems; Compound matrices
                 and determinants: dual theorems; Special determinants:
                 alternant, persymmetric, bigradient, centrosymmetric,
                 Jacobian, Hessian, Wronskian.",
}

@Book{Anonymous:1960:MMS,
  author =       "Anonymous",
  title =        "Mathematical Methods in the Social Sciences, 1959",
  publisher =    pub-STANFORD,
  address =      pub-STANFORD:adr,
  pages =        "viii + 365",
  year =         "1960",
  LCCN =         "????",
  MRclass =      "90.00 (92.00)",
  MRnumber =     "0114658 (22 \#5478)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Proceedings of the first Stanford Symposium. Stanford
                 Mathematical Studies in the Social Sciences, IV",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Axler:1996:LAD,
  author =       "Sheldon Axler",
  title =        "Linear Algebra Done Right",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xviii + 238",
  year =         "1996",
  ISBN =         "0-387-94595-4 (hardcover), 0-387-94596-2 (paperback)",
  ISBN-13 =      "978-0-387-94595-8 (hardcover), 978-0-387-94596-5
                 (paperback)",
  LCCN =         "QA184 .A96 1996",
  MRclass =      "15-01 (47-01)",
  MRnumber =     "1391966 (97i:15002)",
  MRreviewer =   "S. Lajos",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Undergraduate Texts in Mathematics",
  URL =          "http://www.zentralblattmath.org/zmath/en/search/?an=0843.15002",
  ZMnumber =     "0843.15002",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "valeur propre matrice; polyn{\^o}me;
                 d{\'e}composition; vari{\'e}t{\'e} complexe; espace
                 vectoriel; valeur propre; alg{\`e}bre lin{\'e}aire;
                 Alg{\`e}bre lin{\'e}aire; valeur propre matrice;
                 polyn{\^o}me; d{\'e}composition; vari{\'e}t{\'e}
                 complexe; espace vectoriel; valeur propre; alg{\`e}bre
                 lin{\'e}aire.",
  tableofcontents = "Preface to the Instructor / ix \\
                 Preface to the Student / xv \\
                 Acknowledgments / xvii \\
                 Chapter 1 \\
                 Vector Spaces / 1 \\
                 Complex Numbers / 2 \\
                 Definition of Vector Space / 4 \\
                 Properties of Vector Spaces / 10 \\
                 Subspaces / 12 \\
                 Sums and Direct Sums / 13 \\
                 Exercises / 18 \\
                 Chapter 2 \\
                 Finite-Dimensional Vector Spaces / 21 \\
                 Span and Linear Independence / 22 \\
                 Bases / 27 \\
                 Dimension / 30 \\
                 Exercises / 35 \\
                 Chapter 3 \\
                 Linear Maps / 37 \\
                 Definitions and Examples / 38 \\
                 Null Spaces and Ranges / 41 \\
                 The Matrix of a Linear Map / 48 \\
                 Invertibility / 53 \\
                 Exercises / 58 \\
                 Chapter 4 \\
                 Polynomials / 61 \\
                 Degree / 62 \\
                 Complex Coefficients / 65 \\
                 Real Coefficients / 67 \\
                 Exercises / 71 \\
                 Chapter 5 \\
                 Eigenvalues and Eigenvectors / 73 \\
                 Invariant Subspaces / 74 \\
                 Polynomials Applied to Operators / 11 \\
                 Upper-Triangular Matrices / 79 \\
                 Invariant Subspaces on Real Vector Spaces / 85 \\
                 Exercises / 89 \\
                 Chapter 6 \\
                 Inner-Product Spaces / 91 \\
                 Inner Products / 92 \\
                 Norms / 96 \\
                 Orthonormal Bases / 100 \\
                 Orthogonal Projections / 105 \\
                 Exercises / 109 \\
                 Chapter 7 \\
                 Operators on Inner-Product Spaces / 113 \\
                 Linear Functionals and Adjoints / 114 \\
                 Self-Adjoint Operators / 118 \\
                 Normal Operators / 124 \\
                 Positive Operators / 135 \\
                 Isometries / 137 \\
                 Polar and Singular-Value Decompositions / 142 \\
                 Exercises / 148 \\
                 Chapter 8 \\
                 Operators on Complex Vector Spaces / 153 \\
                 Generalized Eigenvectors / 154 \\
                 The Characteristic Polynomial / 158 \\
                 Decomposition of an Operator / 163 \\
                 Square Roots / 166 \\
                 The Minimal Polynomial / 168 \\
                 Jordan Form / 172 \\
                 Exercises / 177 \\
                 Chapter 9 \\
                 Operators on Real Vector Spaces / 181 \\
                 Eigenvalues of Square Matrices / 182 \\
                 Block Upper-Triangular Matrices / 183 \\
                 The Characteristic Polynomial / 186 \\
                 Exercises / 198 \\
                 Chapter 10 \\
                 Trace and Determinant / 201 \\
                 Change of Basis / 202 \\
                 Trace / 204 \\
                 Determinant of an Operator / 210 \\
                 Determinant of a Matrix / 213 \\
                 Volume / 224 \\
                 Exercises / 232 \\
                 Symbol Index / 235 \\
                 Index / 237",
}

@Book{Bapat:1993:LAL,
  author =       "R. B. Bapat",
  title =        "Linear Algebra and Linear Models",
  publisher =    "Hindustan Book Agency",
  address =      "Delhi, India",
  pages =        "viii + 124",
  year =         "1993",
  ISBN =         "81-85931-00-3",
  ISBN-13 =      "978-81-85931-00-5",
  LCCN =         "QA184 .B37 1993",
  MRclass =      "62J05 (15-01); 62J05, 15-01, 62-01, 62J12, 62K05",
  MRnumber =     "1274920 (95e:62071)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Texts and Readings in Mathematics",
  URL =          "http://www.zentralblattmath.org/zmath/en/search/?an=0834.62062",
  ZMnumber =     "0834.62062",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Algebras, Linear; Multivariate analysis",
}

@Book{Bapat:1997:NMA,
  author =       "R. B. Bapat and T. E. S. Raghavan",
  title =        "Nonnegative Matrices and Applications",
  volume =       "64",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xiv + 336",
  year =         "1997",
  DOI =          "https://doi.org/10.1017/CBO9780511529979",
  ISBN =         "0-521-57167-7 (hardcover), 1-107-09513-1,
                 0-511-52997-X (e-book)",
  ISBN-13 =      "978-0-521-57167-8 (hardcover), 978-1-107-09513-7,
                 978-0-511-52997-9 (e-book)",
  LCCN =         "QA188 .B355 1997",
  MRclass =      "15A48 (90A14 90C08); 15A48, 05B20, 15-02, 15A12,
                 15A45, 15A51, 60J10, 91A20, 91B60",
  MRnumber =     "1449393 (98h:15038)",
  MRreviewer =   "J. Parida",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Encyclopedia of Mathematics and its Applications",
  ZMnumber =     "0879.15015",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Matrix; (Math.); Graphentheorie; Graphentheorie;
                 Matrix (Math.); Kombinatorik; Kombinatorik;
                 Matrizentheorie; Nichtnegative Matrix.",
  tableofcontents = "Preface / xi \\
                 1 Perron--Frobenius theory and matrix games / 1 \\
                 1.1 Irreducible nonnegative matrices / 1 \\
                 1.2 Perron's Theorem on positive matrices / 4 \\
                 1.3 Completely mixed games / 7 \\
                 1.4 The Perron--Frobenius theorem / 15 \\
                 1.5 Nonsingular M-matrices / 24 \\
                 1.6 Polyhedral sets with least elements / 30 \\
                 1.7 Reducible nonnegative matrices / 34 \\
                 1.8 Primitive matrices / 40 \\
                 1.9 Finite Markov chains / 44 \\
                 1.10 Self maps of the Lorentz cone / 51 \\
                 Exercises / 54 \\
                 2 Doubly stochastic matrices / 59 \\
                 2.1 The Birkhoff--von Neumann Theorem / 59 \\
                 2.2 Fully indecomposable matrices / 66 \\
                 2.3 Konig's Theorem and rank / 69 \\
                 2.4 The optimal assignment problem / 72 \\
                 2.5 A probabilistic algorithm / 78 \\
                 2.6 Diagonal products / 80 \\
                 2.7 A self map of doubly stochastic matrices / 83 \\
                 2.8 van der Waerden conjecture and its solution / 88
                 \\
                 2.9 Cooperative games with side payments / 94 \\
                 2.10 Lexicographic center / 98 \\
                 2.11 Open shop scheduling / 105 \\
                 2.12 A fair division problem / 108 \\
                 Exercises / 111 \\
                 3 Inequalities / 115 \\
                 3.1 Perron root and row sums / 115 \\
                 3.2 Applications of the Information Inequality / 118
                 \\
                 3.3 Inequalities of Levinger and Kingman / 121 \\
                 3.4 Sum-symmetric matrices / 124 \\
                 3.5 Circuit geometric means / 130 \\
                 3.6 The Hadamard Inequality / 134 \\
                 3.7 Inequalities of Fiedler and Oppenheim / 141 \\
                 3.8 Schur power matrix / 145 \\
                 3.9 Majorization inequalities for eigenvalues / 149 \\
                 3.10 The parallel sum / 153 \\
                 3.11 Symmetric function means / 156 \\
                 Exercises / 158 \\
                 4 Conditionally positive definite matrices / 161 \\
                 4.1 Distance matrices / 161 \\
                 4.2 Quasi-convex quadratic forms / 165 \\
                 4.3 An interpolation problem / 173 \\
                 4.4 A characterization theorem / 177 \\
                 4.5 Log-concavity and discrete distributions / 184 \\
                 4.6 The $q$-permanent / 189 \\
                 Exercises / 193 \\
                 5 Topics in combinatorial theory / 196 \\
                 5.1 Matroids / 196 \\
                 5.2 Mixed discriminants / 200 \\
                 5.3 The Alexandroff Inequality / 203 \\
                 5.4 Coxeter graphs / 209 \\
                 5.5 Matrices over the max algebra / 219 \\
                 5.6 Boolean matrices / 225 \\
                 Exercises / 235 \\
                 6 Scaling problems and their applications / 239 \\
                 6.1 Practical examples of scaling problems / 243 \\
                 6.2 Kronecker Index Theorem and scaling / 247 \\
                 6.3 Hilbert's projective metric / 251 \\
                 6.4 Algorithms for scaling / 261 \\
                 6.5 Maximum likelihood estimation / 263 \\
                 Exercises / 272 \\
                 7 Special matrices in economic models / 275 \\
                 7.1 Pure exchange economy / 276 \\
                 7.2 Linear slave economies / 279 \\
                 7.3 Substitution Theorem / 281 \\
                 7.4 Sraffa system / 282 \\
                 7.5 Dual Sraffa system on quantities / 285 \\
                 7.6 A linear model of an expanding economy / 287 \\
                 7.7 Factor price equalization / 290 \\
                 7.8 $P$-matrices / 293 \\
                 7.9 $N$-matrices / 298 \\
                 7.10 Global univalence / 302 \\
                 7.11 Stability and market prices / 305 \\
                 7.12 Historical notes / 310 \\
                 Exercises / 312 \\
                 References / 315 \\
                 Index / 329 \\
                 Author Index 333",
}

@Book{Barnett:1970:MMSa,
  author =       "S. Barnett and C. Storey",
  title =        "Matrix Methods in Stability Theory",
  publisher =    pub-BN,
  address =      pub-BN:adr,
  pages =        "viii + 148",
  year =         "1970",
  LCCN =         "QA263 .B33 1970",
  bibdate =      "Fri Nov 21 07:39:32 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Applications of mathematics series",
  acknowledgement = ack-nhfb,
  subject =      "Matrices; Lyapunov functions; Stability; Differential
                 equations",
}

@Book{Barnett:1970:MMSb,
  author =       "S. Barnett and C. Storey",
  title =        "Matrix Methods in Stability Theory",
  publisher =    "Nelson",
  address =      "London, UK",
  pages =        "viii + 148",
  year =         "1970",
  ISBN =         "0-17-761617-2",
  ISBN-13 =      "978-0-17-761617-4",
  LCCN =         "QA263 .B33 1970",
  bibdate =      "Fri Nov 21 07:39:32 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Applications of mathematics series",
  acknowledgement = ack-nhfb,
  subject =      "Matrices; Lyapunov functions; Stability; Differential
                 equations",
}

@Book{Barnett:1975:IMC,
  author =       "Stephen Barnett",
  title =        "Introduction to Mathematical Control Theory",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "viii + 264",
  year =         "1975",
  ISBN =         "0-19-859618-9",
  ISBN-13 =      "978-0-19-859618-9",
  LCCN =         "QA402.3 .B347",
  MRclass =      "93-01 (49-01)",
  MRnumber =     "0441413 (55 \#14276)",
  MRreviewer =   "Zvi Artstein",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Oxford Applied Mathematics and Computing Science
                 Series",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Barnett:1979:MME,
  author =       "S. Barnett",
  title =        "Matrix Methods for Engineers and Scientists",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xi + 185",
  year =         "1979",
  ISBN =         "0-07-084084-9",
  ISBN-13 =      "978-0-07-084084-3",
  LCCN =         "QA188 .B37",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Matrices",
}

@Book{Barnett:1983:PLC,
  author =       "Stephen Barnett",
  title =        "Polynomials and Linear Control Systems",
  volume =       "77",
  publisher =    pub-DEKKER,
  address =      pub-DEKKER:adr,
  pages =        "xi + 452",
  year =         "1983",
  ISBN =         "0-8247-1898-4 (hardcover), 0-8247-2898-4",
  ISBN-13 =      "978-0-8247-1898-5 (hardcover), 978-0-8247-2898-4",
  LCCN =         "QA161.P59 B37 1983",
  MRclass =      "93-01 (13F20 93Bxx 93C05)",
  MRnumber =     "704016 (85c:93001)",
  MRreviewer =   "Bradley W. Dickinson",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Monographs and Textbooks in Pure and Applied
                 Mathematics",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1938--",
  subject =      "Polynomials; System analysis; Linear control systems;
                 Kontrolltheorie; Lineares Regelungssystem; Polynom;
                 Systemanalyse; Linear control systems; Polynomials;
                 System analysis.",
  tableofcontents = "Preface / v \\
                 Polynomials: Approaches to Greatest Common Divisor \\
                 1.0 Introduction / 1 \\
                 1.1 Review of Basic Concepts / 2 \\
                 Problems / 8 \\
                 1.2 Companion Matrix and Properties / 10 \\
                 Problems / 20 \\
                 1.3 G.C.D. Using Companion Matrix / 23 \\
                 Problems / 30 \\
                 1.4 Sylvester's Resultant Matrix / 31 \\
                 Problems / 42 \\
                 1.5 B{\'e}zoutian Matrix / 44 \\
                 Problems / 51 \\
                 1.6 Recursive Algorithms / 51 \\
                 1.6.1 The Routh Array / 51 \\
                 1.6.2 An Alternative Array / 57 \\
                 1.6.3 Coefficient Growth / 59 \\
                 1.6.4 The Equation $a x + b y$ / 62 \\
                 Problems / 64 \\
                 Bibliographical Notes / 66 \\
                 2 Basic Properties of Control Systems / 70 \\
                 2.0 Introduction / 70 \\
                 2.1 State Space Concepts / 71 \\
                 Problems / 79 \\
                 2.2 Controllability and Observability / 82 \\
                 Problems / 96 \\
                 2.3 Relationships with Polynomials / 100 \\
                 Problems / 107 \\
                 2.4 Canonical Forms: Single Input and Output / 108 \\
                 Problems / 115 \\
                 2.5 Realization of Transfer Functions / 117 \\
                 Problems / 122 \\
                 2.6 Scalar Linear State Feedback / 123 \\
                 Problems / 128 \\
                 Bibliographical Notes / 130 \\
                 3 Root Location and Stability / 133 \\
                 3.0 Introduction / 133 \\
                 3.1 Stability of Linear Systems / 134 \\
                 Problems / 140 \\
                 3.2 Root Location and Stability Criteria / 141 \\
                 3.2.1 Real Continuous-Time Case / 141 \\
                 3.2.2 Real Discrete-Time Case / 165 \\
                 3.2.3 Complex Polynomials / 179 \\
                 3.2.4 Recapitulation / 189 \\
                 Problems / 190 \\
                 3.3 Some Key Proofs / 195 \\
                 3.3.1 Matrix Equation Approach: Continuous-Time Case /
                 195 \\
                 3.3.2 Matrix Equation Approach: Discrete-Time Case /
                 215 \\
                 3.3.3 Alternative Proof of the Complex Schur--Cohn
                 Theorem / 219 \\
                 Problems / 222 \\
                 3.4 Cauchy Index Method / 226 \\
                 Problems / 236 \\
                 3.5 Additional Topics / 237 \\
                 3.5.1 Bilinear Transformation / 237 \\
                 3.5.2 Other Regions of the Complex Plane / 243 \\
                 Problems / 249 \\
                 Bibliographical Notes / 251 \\
                 4 Feedback, Realization, and Polynomial Matrices / 259
                 \\
                 4.0 Introduction / 259 \\
                 4.1 Linear Feedback / 261 \\
                 4.1.1 Eigenvalue Assignment by State Feedback / 261 \\
                 4.1.2 Canonical Forms / 273 \\
                 4.1.3 Optimal Quadratic Regulator / 279 \\
                 4.1.4 Output Feedback and Observers / 288 \\
                 Problems / 295 \\
                 4.2 Transfer Function Matrices / 302 \\
                 4.2.1 Definitions / 302 \\
                 4.2.2 State Space Realization / 305 \\
                 4.2.3 Matrix-Fraction Description / 316 \\
                 Problems / 332 \\
                 4.3 Relative Primeness and G.C.D. for Polynomial
                 Matrices / 334 \\
                 4.3.1 Definitions / 334 \\
                 4.3.2 Relatively Prime Determinants / 336 \\
                 4.3.3 Resultants for Prime Matrices / 345 \\
                 4.3.4 G.C.D. of Polynomial Matrices / 353 \\
                 Problems / 360 \\
                 Bibliographical Notes / 363 \\
                 5 Generalized Polynomials and Polynomial Matrices / 369
                 \\
                 5.0 Introduction / 369 \\
                 5.1 Congenial Matrices / 370 \\
                 5.1.1 Orthogonal Basis: Comrade and Colleague / 370 \\
                 5.1.2 Confederate Matrix / 378 \\
                 Problems / 382 \\
                 5.2 Greatest Common Divisors / 384 \\
                 5.2.1 G.C.D. Using Congenial Matrices / 384 \\
                 5.2.2 Routh-Type Tabular Scheme / 393 \\
                 5.2.3 Polynomial Matrices / 399 \\
                 Problems / 400 \\
                 5.3 Applications to Linear Control Systems / 402 \\
                 Problems / 408 \\
                 5.4 Other Applications / 409 \\
                 Problems / 411 \\
                 Bibliographical Notes / 412 \\
                 Appendix A: Kronecker Product and Matrix Functions /
                 415 \\
                 Appendix B: Notation / 419 \\
                 References / 421 \\
                 Answers to Problems / 445 \\
                 Index / 449",
}

@Book{Barnett:1985:IMC,
  author =       "Stephen Barnett and R. G. Cameron",
  title =        "Introduction to Mathematical Control Theory",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  edition =      "Second",
  pages =        "xi + 404",
  year =         "1985",
  ISBN =         "0-19-859640-5, 0-19-859639-1 (paperback)",
  ISBN-13 =      "978-0-19-859640-0, 978-0-19-859639-4 (paperback)",
  LCCN =         "QA402.3 .B347 1985",
  bibdate =      "Sat Nov 22 18:12:06 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Oxford applied mathematics and computing science
                 series",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002139017.pdf;
                 http://www.loc.gov/catdir/enhancements/fy0640/85021589-d.html",
  abstract =     "In this new edition of a successful text, Professor
                 Barnett, now joined in the authorship by Dr. Cameron,
                 has concentrated on adding material where topics have
                 developed since the first edition, and they have also
                 taken advantage of the extensive classroom testing that
                 has been possible in the intervening years. The book
                 remains the concise readable account of some basic
                 mathematical aspects of control, concentrating on
                 state-space methods and emphasizing points of
                 mathematical interest. As far as the additional
                 material is concerned, the new chapter on multivariable
                 theory reflects some of the significant developments in
                 that field during the past decade, and there is also
                 now an appendix on Kalman filtering. All references
                 have been updated and a large number of new problems
                 for student use have been incorporated.",
  acknowledgement = ack-nhfb,
  subject =      "Control theory; Commande; Syst{\`e}me lin{\'e}aire;
                 Stabilit{\'e}; Commande optimale; Diagramme Nyquist;
                 Control theory.; Commande, Th{\'e}orie de la.",
  tableofcontents = "1. Introduction to Control Theory \\
                 1.1. General remarks and examples / 1 \\
                 1.2. Classical control and transform theory \\
                 1.2.1. Continuous-time systems: Laplace transform / 11
                 \\
                 1.2.2. Discrete-time systems: $z$-transform / 16 \\
                 Additional problems / 22 \\
                 2. Preliminary Matrix Theory \\
                 2.1. Definitions / 26 \\
                 2.2. Linear dependence and rank / 30 \\
                 2.3. Polynomials / 34 \\
                 2.4. Characteristic roots (eigenvalues) / 35 \\
                 2.5. Polynomial and rational matrices / 42 \\
                 2.6. Jordan canonical form / 51 \\
                 2.7. Functions of a matrix / 54 \\
                 2.8. Quadratic and Hermitian forms / 58 \\
                 2.9. Gaussian elimination / 62 \\
                 3. Matrix Solution of Linear Systems \\
                 3.1. Solution of uncontrolled system: spectral form /
                 65 \\
                 3.2. Solution of uncontrolled system: exponential
                 matrix / 68 \\
                 3.3. Solution of uncontrolled system: repeated roots /
                 72 \\
                 3.4. Solution of controlled system / 74 \\
                 3.5. Time varying systems / 76 \\
                 3.6. Discrete-time systems / 79 \\
                 3.7. Relationships between state space and classical
                 forms / 84 \\
                 Additional problems / 93 \\
                 4. Linear Control Systems \\
                 4.1. Controllability / 97 \\
                 4.2. Observability / 111 \\
                 4.3. Controllability and polynomials / 119 \\
                 4.4. Linear feedback / 122 \\
                 4.5. State observers / 134 \\
                 4.6. Realization of constant systems / 137 \\
                 4.7. Discrete-time systems / 153 \\
                 4.8. Realization of time varying systems / 157 \\
                 Additional problems / 161 \\
                 5. Stability \\
                 5.1. Definitions / 169 \\
                 5.2. Algebraic criteria for linear systems \\
                 5.2.1. Continuous-time / 177 \\
                 5.2.2. Discrete-time / 186 \\
                 5.2.3. Time varying / 191 \\
                 5.3. Nyquist criterion for linear systems / 195 \\
                 5.4. Liapunov theory / 204 \\
                 5.5. Application of Liapunov theory to linear systems /
                 213 \\
                 5.6. Construction of Liapunov functions \\
                 5.6.1. Variable gradient method / 221 \\
                 5.6.2. Zubov's method / 224 \\
                 5.7. Stability and control \\
                 5.7.1. Input-output stability / 226 \\
                 5.7.2. Linear feedback / 228 \\
                 5.7.3. Nonlinear feedback / 230 \\
                 Additional problems / 238 \\
                 6. Optimal Control \\
                 6.1. Performance indices \\
                 6.1.1. Measures of performance / 245 \\
                 6.1.2. Evaluation of quadratic indices / 248 \\
                 6.2. Calculus of variations / 252 \\
                 6.3. Pontryagin's principle / 263 \\
                 6.4. Linear regulator / 275 \\
                 Additional problems / 284 \\
                 7. Multivariable Systems: The Frequency-domain Approach
                 \\
                 7.1. Poles and zeros of the internal model / 291 \\
                 7.2. Poles and zeros of the external model / 305 \\
                 7.2.1. Definition via the Smith--McMillan form / 306
                 \\
                 7.2.2. Matrix-fraction description / 309 \\
                 7.3. Generalizations of the Nyquist diagram \\
                 7.3.1. Characteristic gain and characteristic frequency
                 functions / 318 \\
                 7.3.2. Algebraic functions and the Riemann surface /
                 322 \\
                 7.3.3. Poles and zeros: characteristic gain and
                 frequency loci / 323 \\
                 7.3.4. The inverse Nyquist array / 332 \\
                 7.4. Design of multivariable controllers \\
                 7.4.1. Preamble: the design problem and objectives /
                 340 \\
                 7.4.2. The inverse Nyquist array method / 343 \\
                 7.4.3. The characteristic locus method / 355 \\
                 Additional problems / 369 \\
                 Appendix: The Kalman--Bucy filter / 374 \\
                 References / 379 \\
                 Answers to Exercises / 383 \\
                 Answers to Additional Problems / 392 \\
                 Index / 400",
}

@Book{Barnett:1990:MMA,
  author =       "Stephen Barnett",
  title =        "Matrices: Methods and Applications",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xvi + 450",
  year =         "1990",
  ISBN =         "0-19-859665-0, 0-19-859680-4 (paperback)",
  ISBN-13 =      "978-0-19-859665-3, 978-0-19-859680-6 (paperback)",
  LCCN =         "QA188 .B36 1990",
  MRclass =      "15-01 (15-02 65-01 90-02 93-02); 15-01, 15A03, 15A06,
                 15A09, 15A18, 15A21, 15A24, 15A60, 15A63, 65F05",
  MRnumber =     "1076364 (92d:15001)",
  MRreviewer =   "Michael J. C. Gover",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Oxford Applied Mathematics and Computing Science
                 Series",
  URL =          "http://catdir.loc.gov/catdir/enhancements/fy0603/89023942-d.html;
                 http://catdir.loc.gov/catdir/enhancements/fy0603/89023942-t.html;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0706.15001",
  ZMnumber =     "0706.15001",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "1. How Matrices Arise \\
                 2. Basic Algebra of Matrices \\
                 3. Unique Solution to Linear Equations \\
                 4. Determinant and Inverse \\
                 5. Rank, Non-Unique Solution of Equations, and
                 Applications \\
                 6. Eigenvalues and Eigenvectors \\
                 7. Quadratic and Hermitian Forms \\
                 8. Canonical Forms \\
                 9. Matrix Functions \\
                 10. Generalized Inverses \\
                 11. Polynomials, Stability, and Matrix Equations \\
                 12. Polynomial and Rational Matrices \\
                 13. Patterned Matrices \\
                 14. Miscellaneous Topics",
}

@Book{Baumgartel:1985:APT,
  author =       "H. Baumg{\"a}rtel",
  title =        "Analytic Perturbation Theory for Matrices and
                 Operators",
  volume =       "15",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "427",
  year =         "1985",
  ISBN =         "3-7643-1664-0",
  ISBN-13 =      "978-3-7643-1664-8",
  LCCN =         "QA188 .B38 1985",
  MRclass =      "47A55",
  MRnumber =     "878974 (88a:47016)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Operator Theory: Advances and Applications",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002465460.pdf",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Matrices; Linear operators; Perturbation
                 (Mathematics); Linear operators; Matrices; Perturbation
                 (Mathematics); Matrizenrechnung; Operator;
                 St{\"o}rungstheorie",
  tableofcontents = "Introduction / 19 \\
                 1. Finite-dimensional linear analysis / 27 \\
                 2. Spectral theory and Jordan structure of linear
                 operators / 57 \\
                 3. Spectral theory of meromorphic operator-valued
                 functions / 98 \\
                 4. Linear operators on linear spaces over commutative
                 fields; first applications / 167 \\
                 5. Jordan structure of meromorphic operator-valued
                 functions / 195 \\
                 6. Analytic perturbations / 227 \\
                 7. Reduction theory / 242 \\
                 8. Numerical analysis for perturbation series ---
                 convergence radii and error estimates / 321 \\
                 9. Polynomial operator-valued functions / 341 \\
                 10. Analytic perturbations in Banach spaces / 357 \\
                 Supplement. Analytic perturbations for linear operators
                 depending on several complex variables / 371 \\
                 Appendix. Basic material from complex function theory
                 and algebra / 388 \\
                 Bibliography / 415 \\
                 Articles / 415 \\
                 Books and monographs / 420\\
                 Subject index / 424",
}

@Book{Beckenbach:1965:I,
  author =       "Edwin F. Beckenbach and Richard Bellman",
  title =        "Inequalities",
  volume =       "30",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 198",
  year =         "1965",
  LCCN =         "????",
  MRclass =      "26.70 (26.00)",
  MRnumber =     "0192009 (33 \#236)",
  MRreviewer =   "J. Acz{\'e}l",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Second revised printing. Ergebnisse der Mathematik und
                 ihrer Grenzgebiete. Neue Folge",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Belitskii:1988:MNT,
  author =       "Genrikh Ruvimovich Belitski{\u\i} and Yuri Ilich
                 Lyubich",
  title =        "Matrix Norms and Their Applications",
  volume =       "36",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "viii + 209",
  year =         "1988",
  DOI =          "https://doi.org/10.1007/978-3-0348-7400-7",
  ISBN =         "3-7643-2220-9 (Basel), 0-8176-2220-9 (Boston)",
  ISBN-13 =      "978-3-7643-2220-5 (Basel), 978-0-8176-2220-6
                 (Boston)",
  LCCN =         "QA188 .B4313 1988",
  MRclass =      "15-02 (00A69 15A60 47-02 65F35); 15A60, 06F25, 15-01,
                 15A18, 60J10",
  MRnumber =     "1015711 (90g:15003)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Translated from the Russian by A. Iacob.",
  series =       "Operator Theory: Advances and Applications",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht003195543.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0645.15019",
  ZMnumber =     "0645.15019",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface / vii \\
                 Chapter 1: Operators in Finite-Dimensional Normed
                 Spaces / 1 \\
                 1. Norms of vectors, linear functionals, and linear
                 operators / 1 \\
                 2. Survey of spectral theory / 14 \\
                 3. Spectral radius / 17 \\
                 4. One-parameter groups and semigroups of operators /
                 25 \\
                 Appendix. Conditioning in general computational
                 problems / 28 \\
                 Chapter 2: Spectral Properties of Contractions / 33 \\
                 1. Contractive operators and isometries / 33 \\
                 2. Stability theorems / 46 \\
                 3. One-parameter semigroups of contractions and groups
                 of isometries / 48 \\
                 4. The boundary spectrum of extremal contractions / 52
                 \\
                 5. Extreme points of the unit ball in the space of
                 operators / 64 \\
                 6. Critical exponents / 66 \\
                 7. The apparatus of functions on graphs / 72 \\
                 8. Combinatorial and spectral properties of
                 $\ell_\infty$-contractions / 81 \\
                 9. Combinatorial and spectral properties of nonnegative
                 matrices / 96 \\
                 10. Finite Markov chains / 102 \\
                 11. Nonnegative projectors / 108 \\
                 Chapter 3: Operator Norms / 113 \\
                 1. Ring norms on the algebra of operators in $E$ / 113
                 \\
                 2. Characterization of operator norms / 126 \\
                 3. Operator minorants / 133 \\
                 4. Suprema of families of operator norms / 141 \\
                 5. Ring cross-norms / 150 \\
                 6. Orthogonally-invariant norms / 152 \\
                 Chapter 4: Study of the Order Structure on the Set of
                 Ring Norms / 157 \\
                 1. Maximal chains of ring norms / 157 \\
                 2. Generalized ring norms / 160 \\
                 3. The lattice of subalgebras of the algebra End($E$) /
                 166 \\
                 4. Characterization of automorphisms / 179 \\
                 Brief Comments on the Literature / 201 \\
                 References / 205",
}

@Book{Bellman:1970:IMA,
  author =       "Richard Bellman",
  title =        "Introduction to Matrix Analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "xxiii + 403",
  year =         "1970",
  LCCN =         "????",
  MRclass =      "15.00",
  MRnumber =     "0258847 (41 \#3493)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Berman:1979:NMM,
  author =       "Abraham Berman and Robert J. Plemmons",
  title =        "Nonnegative Matrices in the Mathematical Sciences",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xviii + 316",
  year =         "1979",
  DOI =          "https://doi.org/10.1016/B978-0-12-092250-5.50018-7",
  ISBN =         "0-12-092250-9",
  ISBN-13 =      "978-0-12-092250-5",
  LCCN =         "QA188.B47 1979",
  bibdate =      "Sat Nov 22 13:54:22 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Computer Science and Applied Mathematics.",
  URL =          "http://www.sciencedirect.com/science/book/9780120922505",
  abstract =     "Matrices which leave a cone invariant; Nonnegative
                 matrices; Semigroups of nonnegative matrices; Symmetric
                 nonnegative matrices; Generalized inverse-positivity;
                 M-Matrices; Iterative methods for linear systems;
                 Finite Markov chains; Input-output analysis in
                 economics; The linear complementarity problem.",
  acknowledgement = ack-nhfb,
  subject =      "Non-negative matrices; compl{\'e}mentarit{\'e};
                 matrice M; syst{\`e}me lin{\'e}aire; semi-groupe;
                 cha{\^i}ne Markov; programmation lin{\'e}aire; matrice
                 non n{\'e}gative; Matrices non n{\'e}gatives;
                 Matrices.; Lineaire algebra.; Matrices
                 nonn{\'e}gatives.; Matrizenrechnung.; Non-negative
                 matrices.",
  tableofcontents = "Dedication / v \\
                 Preface / xi--xiii \\
                 Acknowledgments / xv \\
                 Symbols / xvii--xviii \\
                 1: Matrices Which Leave a Cone Invariant / 1--25 \\
                 2: Nonnegative Matrices / 26--62 \\
                 3: Semigroups of Nonnegative Matrices / 63--86 \\
                 \\
                 4: Symmetric Nonnegative Matrices / 87--111 \\
                 5: Generalized Inverse-Positivity / 112--131 \\
                 6: $M$-Matrices / 132--164 \\
                 7: Iterative Methods for Linear Systems / 165--209 \\
                 8: Finite Markov Chains / 210--241 \\
                 9: Input Output Analysis in Economics / 242--269 \\
                 10: The Linear Complementarity Problem / 270--297 \\
                 References / 298--312 \\
                 Index / 313--316",
}

@Book{Berman:1989:NMD,
  author =       "Abraham Berman and Michael Neumann and Ronald J.
                 Stern",
  title =        "Nonnegative Matrices in Dynamic Systems",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xxii + 167",
  year =         "1989",
  ISBN =         "0-471-62074-2 (hardcover)",
  ISBN-13 =      "978-0-471-62074-7 (hardcover)",
  LCCN =         "QA188 .B466 1989",
  MRclass =      "93B25 (15A48 34A30 93-02 93C35)",
  MRnumber =     "1019319 (90j:93030)",
  MRreviewer =   "K. B. Datta",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Pure and Applied Mathematics (New York)",
  URL =          "http://catdir.loc.gov/catdir/description/wiley031/88033934.html;
                 http://www.gbv.de/dms/hbz/toc/ht003360524.pdf;
                 http://www.loc.gov/catdir/description/wiley031/88033934.html;
                 http://www.loc.gov/catdir/toc/onix02/88033934.html;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0723.93013",
  ZMnumber =     "0723.93013",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "Michael Neumann (1946--)",
  subject =      "Matrices nonn{\'e}gatives; Syst{\`e}mes, Analyse de;
                 Non-negative matrices; System analysis; commande
                 r{\'e}troactive; analyse syst{\`e}me; syst{\`e}me
                 dynamique; matrice non n{\'e}gative",
  tableofcontents = "Preface / ix \\
                 Acknowledgments / xv \\
                 List of Symbols / xvii \\
                 1. Convex sets \\
                 1. Introduction / 1 \\
                 2. Convex sets and cones / 1 \\
                 3. Functions valued in a convex set / 6 \\
                 4. Notes / 7 \\
                 2. Matrix theory background 9 \\
                 1. Introduction / 9 \\
                 2. The Jordan and real canonical forms / 9 \\
                 3. Nonnegative matrices / 15 \\
                 4. $M$-matrices / 19 \\
                 5. The Frobenius normal form / 24 \\
                 6. Notes / 29 \\
                 3. Differential and control system preliminaries / 31
                 \\
                 1. Introduction / 31 \\
                 2. linear differential systems / 31 \\
                 3. linear control systems: controllability.
                 observability. and realizability / 35 \\
                 4. Glossary of models / 54 \\
                 5. Notes / 58 \\
                 4. Exponentially nonnegative matrices / 61 \\
                 1. Introduction / 61 \\
                 2. Holdable closed convex sets: geometric
                 considerations / 65 \\
                 3. Exponentially nonnegative matrices / 70 \\
                 4. Notes / 83 \\
                 5. Extended $M$-matrices / 85 \\
                 1. Introduction / 85 \\
                 2. Extended $M$-matrices / 86 \\
                 3. Further results / 88 \\
                 4. Notes / 91 \\
                 6. Cone reachability / 93 \\
                 1. Introduction / 93 \\
                 2. Basic properties of reachability cones / 94 \\
                 3. Cone reachability: simple cases / 98 \\
                 4. Cone reachability: the case of a real spectrum / 102
                 \\
                 5. The boundary of the reachability cone / 110 \\
                 6. Cone reachability for discrete approximations to the
                 differential equation / 115 \\
                 7. Notes / 124 \\
                 7. Applications to feedback control / 125 \\
                 1. Introduction / 125 \\
                 2. Feedback holdability of $R^n_+$ / 126 \\
                 3. Controllability to $R^n_+$ / 129 \\
                 4. A stabilizability--holdability problem / 132 \\
                 5. Notes / 134 \\
                 8. Controllability, observability, and realizability of
                 positive control systems / 137 \\
                 1. Introduction / 137 \\
                 2. Controllability with nonnegative controls / 137 \\
                 3. Observability with conical observation set / 146 \\
                 4. Positive realization / 155 \\
                 5. Notes / 159 \\
                 References / 161 \\
                 Index / 165",
}

@Book{Berman:1994:NMM,
  author =       "Abraham Berman and Robert J. Plemmons",
  title =        "Nonnegative Matrices in the Mathematical Sciences",
  volume =       "9",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xx + 340",
  year =         "1994",
  DOI =          "https://doi.org/10.1137/1.9781611971262",
  ISBN =         "0-89871-321-8",
  ISBN-13 =      "978-0-89871-321-3",
  LCCN =         "QA188 .B47 1994",
  MRclass =      "15A48 (15-02 60J10 90C33)",
  MRnumber =     "1298430 (95e:15013)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  note =         "Revised reprint of \cite{Berman:1979:NMM}.",
  series =       "Classics in Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0708/94037449-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0708/94037449-t.html",
  abstract =     "Here is a valuable text and research tool for
                 scientists and engineers who use or work with theory
                 and computation associated with practical problems
                 relating to Markov chains and queuing networks,
                 economic analysis, or mathematical programming.
                 Originally published in 1979, this new edition adds
                 material that updates the subject relative to
                 developments from 1979 to 1993. Theory and applications
                 of nonnegative matrices are blended here, and extensive
                 references are included in each area. You will be led
                 from the theory of positive operators via the
                 Perron-Frobenius theory of nonnegative matrices and the
                 theory of inverse positivity, to the widely used topic
                 of $M$-matrices. On the way, semigroups of nonnegative
                 matrices and symmetric nonnegative matrices are
                 discussed. Later, applications of nonnegativity and
                 $M$-matrices are given; for numerical analysis the
                 example is convergence theory of iterative methods, for
                 probability and statistics the examples are finite
                 Markov chains and queuing network models, for
                 mathematical economics the example is input-output
                 models, and for mathematical programming the example is
                 the linear complementarity problem. Nonnegativity
                 constraints arise very naturally throughout the
                 physical world. Engineers, applied mathematicians, and
                 scientists who encounter nonnegativity or
                 generalizations of nonnegativity in their work will
                 benefit from topics covered here, connecting them to
                 relevant theory. Researchers in one area, such as
                 queuing theory, may find useful the techniques
                 involving nonnegative matrices used by researchers in
                 another area, say, mathematical programming. Exercises
                 and biographical notes are included with each
                 chapter.",
  acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah # "
                 and " # ack-crj,
  tableofcontents = "1: Matrices Which Leave a Cone Invariant \\
                 2: Nonnegative Matrices \\
                 3: Semigroups of Nonnegative Matrices \\
                 4: Symmetric Nonnegative Matrices \\
                 5: Generalized Inverse-Positivity \\
                 6: $M$-Matrices \\
                 7: Iterative Methods for Linear Systems \\
                 8: Finite Markov Chains \\
                 9: Input-Output Analysis in Economics \\
                 10: The Linear Complementarity Problem \\
                 11: Supplement 1979--1993 \\
                 References \\
                 Index",
}

@Book{Bernstein:2009:MMT,
  author =       "Dennis S. Bernstein",
  title =        "Matrix Mathematics: Theory, Facts, and Formulas",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  edition =      "Second",
  pages =        "xlii + 1139",
  year =         "2009",
  ISBN =         "0-691-13287-9 (hardcover), 0-691-14039-1 (paperback),
                 1-4008-3334-5 (e-book)",
  ISBN-13 =      "978-0-691-13287-7 (hardcover), 978-0-691-14039-1
                 (paperback), 978-1-4008-3334-4 (e-book)",
  LCCN =         "QA188 .B475 2009; QA188 .B475X 2009 (LC)",
  MRclass =      "93-02 (15-01 93B52 93C05)",
  MRnumber =     "2513751 (2010e:93001)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
                 prodorbis.library.yale.edu:7090/voyager;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.jstor.org/stable/10.2307/j.ctt7t833;
                 http://www.loc.gov/catdir/toc/ecip0826/2008036257.html",
  abstract =     "When first published in 2005, \booktitle{Matrix
                 Mathematics} quickly became the essential reference
                 book for users of matrices in all branches of
                 engineering, science, and applied mathematics. In this
                 fully updated and expanded edition, the author brings
                 together the latest results on matrix theory to make
                 this the most complete, current, and easy-to-use book
                 on matrices. Each chapter describes relevant background
                 theory followed by specialized results. Hundreds of
                 identities, inequalities, and matrix facts are stated
                 clearly and rigorously with cross references, citations
                 to the literature, and illuminating remarks. Beginning
                 with preliminaries on sets, functions, and relations,
                 \booktitle{Matrix Mathematics} covers all of the major
                 topics in matrix theory, including matrix
                 transformations; polynomial matrices; matrix
                 decompositions; generalized inverses; Kronecker and
                 Schur algebra; positive-semidefinite matrices; vector
                 and matrix norms; the matrix exponential and stability
                 theory; and linear systems and control theory. Also
                 included are a detailed list of symbols, a summary of
                 notation and conventions, an extensive bibliography and
                 author index with page references, and an exhaustive
                 subject index. This significantly expanded edition of
                 \booktitle{Matrix Mathematics} features a wealth of new
                 material on graphs, scalar identities and inequalities,
                 alternative partial orderings, matrix pencils, finite
                 groups, zeros of multivariable transfer functions,
                 roots of polynomials, convex functions, and matrix
                 norms. Covers hundreds of important and useful results
                 on matrix theory, many never before available in any
                 book. Provides a list of symbols and a summary of
                 conventions for easy use. Includes an extensive
                 collection of scalar identities and inequalities.
                 Features a detailed bibliography and author index with
                 page references. Includes an exhaustive subject index
                 with cross-referencing.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1954--",
  subject =      "Matrices; Linear systems",
  tableofcontents = "1: Preliminaries / 1 \\
                 2: Basic Matrix Properties / 85 \\
                 3: Matrix Classes and Transformations / 179 \\
                 4: Polynomial Matrices and Rational Transfer Functions
                 / 253 \\
                 5: Matrix Decompositions / 309 \\
                 6: Generalized Inverses / 397 \\
                 7: Kronecker and Schur Algebra / 439 \\
                 8: Positive-Semidefinite Matrices / 459 \\
                 9: Norms / 597 \\
                 10: Functions of Matrices and Their Derivatives / 681
                 \\
                 11: The Matrix Exponential and Stability Theory / 707
                 \\
                 12: Linear Systems and Control Theory / 795 \\
                 Bibliography / 881 \\
                 Author Index / 967 \\
                 Index / 979",
}

@Book{Bhatia:1987:PBM,
  author =       "Rajendra Bhatia",
  title =        "Perturbation Bounds for Matrix Eigenvalues",
  volume =       "162",
  publisher =    pub-LONGMAN,
  address =      pub-LONGMAN:adr,
  pages =        "viii + 129",
  year =         "1987",
  ISBN =         "0-470-20917-8 (paperback), 0-582-01379-8 (paperback)",
  ISBN-13 =      "978-0-470-20917-2 (paperback), 978-0-582-01379-7
                 (paperback)",
  ISSN =         "0269-3674",
  LCCN =         "QA193",
  MRclass =      "15A42 (15A60 47A55 65F15); 15A42, 15-02, 15A18,
                 15A57",
  MRnumber =     "925418 (88k:15020)",
  MRreviewer =   "A. R. Amir-Mo{\'e}z",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Pitman Research Notes in Mathematics Series",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002967626.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0696.15013",
  ZMnumber =     "0696.15013",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1952--",
  subject =      "Eigenvalues; Perturbation (Mathematics); Matrices;
                 Valeurs propres; Perturbation (Math{\'e}matiques);
                 Matrices; Eigenwaarden; Eigenvalues; Matrices;
                 Perturbation (Mathematics)",
  tableofcontents = "Preface \\
                 Introduction / 1 \\
                 1. Preliminaries / 7 \\
                 1. The marriage problem / 7 \\
                 2. Birkhoff's theorem / 11 \\
                 3. Majorization / 11 \\
                 4. Tensor products / 14 \\
                 Notes and references / 16 \\
                 2. Singular values and norms / 18 \\
                 5. Singular values and polar decomposition / 18 \\
                 6. The minmax principle / 20 \\
                 7. Symmetric gauge functions and norms / 24 \\
                 Notes and references / 31 \\
                 3. Spectral variation of Hermitian matrices / 34 \\
                 8. Weyl's inequalities / 34 \\
                 9. The Lidskii--Wielandt theorem / 38 \\
                 10. Matrices with real eigenvalues and Lax's theorem /
                 46 \\
                 Notes and references / 50 \\
                 4. Spectral variation of normal matrices / 52 \\
                 11. Introduction to chapter 4 / 52 \\
                 12. The Hausdorff distance between spectra / 53 \\
                 13. Geometry and spectral variation / 55 \\
                 14. Geometry and spectral variation II / 63 \\
                 15. The Hoffman--Wielandt theorem / 74 \\
                 16. Perturbation of spectral spaces / 76 \\
                 17. The cyclic order / 82 \\
                 18. An inequality of Sunder / 85 \\
                 Notes and references / 86 \\
                 5. The general spectral variation problem / 89 \\
                 19. The distance between roots of polynomials / 89 \\
                 20. Variation of Grassmann powers and spectra / 94 \\
                 21. Some more spectral variation bounds / 99 \\
                 22. Spectral variation for the classical Lie algebras /
                 104 \\
                 Notes and references / 105 \\
                 6. Arbitrary perturbations of constrained matrices /
                 108 \\
                 23. Arbitrary perturbations of Hermitian matrices and
                 Kahan's results / 108 \\
                 24. Arbitrary perturbations of normal matrices / 112
                 \\
                 25. The Bauer--Fike theorem / 113 \\
                 Notes and references / 116 \\
                 Postscripts / 118 \\
                 References / 122",
  xxpublisher =  "Longman Scientific \& Technical, Harlow; John Wiley \&
                 Sons, Inc., New York",
}

@Book{Bhatia:1997:MA,
  author =       "Rajendra Bhatia",
  title =        "Matrix Analysis",
  volume =       "169",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 347",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4612-0653-8",
  ISBN =         "0-387-94846-5 (print), 1-4612-0653-7 (e-book)",
  ISBN-13 =      "978-0-387-94846-1 (print), 978-1-4612-0653-8
                 (e-book)",
  LCCN =         "QA188 .B485 1996",
  MRclass =      "15-02 (47-02)",
  MRnumber =     "1477662 (98i:15003)",
  MRreviewer =   "R. J. Bumcrot",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  series =       "Graduate Texts in Mathematics",
  URL =          "http://catdir.loc.gov/catdir/enhancements/fy0818/96032217-d.html;
                 http://www.gbv.de/dms/goettingen/213798093.pdf",
  abstract =     "The aim of this book is to present a substantial part
                 of matrix analysis that is functional analytic in
                 spirit. Much of this will be of interest to graduate
                 students and research workers in operator theory,
                 operator algebras, mathematical physics, and numerical
                 analysis. The book can be used as a basic text for
                 graduate courses on advanced linear algebra and matrix
                 analysis. It can also be used as supplementary text for
                 courses in operator theory and numerical analysis.
                 Among topics covered are the theory of majorization,
                 variational principles of eigenvalues, operator
                 monotone and convex functions, perturbation of matrix
                 functions, and matrix inequalities. Much of this is
                 presented for the first time in a unified way in a
                 textbook. The reader will learn several powerful
                 methods and techniques of wide applicability, and see
                 connections with other areas of mathematics. A large
                 selection of matrix inequalities will make this book a
                 valuable reference for students and researchers who are
                 working in numerical analysis, mathematical physics and
                 operator theory.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface / v \\
                 I A Review of Linear Algebra / 1 \\
                 1.1 Vector Spaces and Inner Product Spaces / 1 \\
                 1.2 Linear Operators and Matrices / 3 \\
                 1.3 Direct Sums / 9 \\
                 1.4 Tensor Products / 12 \\
                 1.5 Symmetry Classes / 16 \\
                 1.6 Problems / 20 \\
                 1.7 Notes and References / 26 \\
                 II Majorisation and Doubly Stochastic Matrices / 28 \\
                 11.1 Basic Notions / 28 \\
                 11.2 Birkhoff's Theorem / 36 \\
                 11.3 Convex and Monotone Functions / 40 \\
                 11.4 Binary Algebraic Operations and Majorisation / 48
                 \\
                 11.5 Problems / 50 \\
                 11.6 Notes and References / 54 \\
                 III Variational Principles for Eigenvalues / 57 \\
                 III.1 The Minimax Principle for Eigenvalues / 57 \\
                 111.2 Weyl's Inequalities / 62 \\
                 111.3 Wielandt's Minimax Principle / 65 \\
                 111.4 Lidskii's Theorems / 68 \\
                 III.5 Eigenvalues of Real Parts and Singular Values /
                 73 \\
                 111.6 Problems / 75 \\
                 111.7 Notes and References / 78 \\
                 IV Symmetric Norms / 84 \\
                 IV.1 Norms on $C^n$ / 84 \\
                 IV.2 Unitarily Invariant Norms on Operators on $C^n$ /
                 91 \\
                 IV.3 Lidskii's Theorem (Third Proof) / 98 \\
                 IV.4 Weakly Unitarily Invariant Norms / 101 \\
                 IV.5 Problems / 107 \\
                 IV.6 Notes and References / 109 \\
                 V Operator Monotone and Operator Convex Functions / 112
                 \\
                 V.1 Definitions and Simple Examples / 112 \\
                 V.2 Some Characterisations / 117 \\
                 V.3 Smoothness Properties / 123 \\
                 V.4 L{\"o}wner's Theorems / 131 \\
                 V.5 Problems / 147 \\
                 V.6 Notes and References / 149 \\
                 VI Spectral Variation of Normal Matrices / 152 \\
                 VI.1 Continuity of Roots of Polynomials / 153 \\
                 VI.2 Hermitian and Skew-Hermitian Matrices / 155 \\
                 VI.3 Estimates in the Operator Norm / 159 \\
                 VI.4 Estimates in the Frobenius Norm / 165 \\
                 VI.5 Geometry and Spectral Variation: the Operator Norm
                 / 168 \\
                 VI.6 Geometry and Spectral Variation: wui Norms / 173
                 \\
                 VI.7 Some Inequalities for the Determinant / 181 \\
                 VI.8 Problems / 184 \\
                 VI.9 Notes and References / 190 \\
                 VII Perturbation of Spectral Subspaces of Normal
                 Matrices / 194 \\
                 VII.1 Pairs of Subspaces / 195 \\
                 VII.2 The Equation $A X -X B = Y$ / 203 \\
                 VII.3 Perturbation of Eigenspaces / 211 \\
                 VII.4 A Perturbation Bound for Eigenvalues / 212 \\
                 VII.5 Perturbation of the Polar Factors / 213 \\
                 VII.6 Appendix: Evaluating the (Fourier) constants /
                 216 \\
                 VII.7 Problems / 221 \\
                 VII.8 Notes and References / 223 \\
                 VIII Spectral Variation of Nonnormal Matrices / 226 \\
                 VIII.1 General Spectral Variation Bounds / 227 \\
                 VIII.4 Matrices with Real Eigenvalues / 238 \\
                 VIII.5 Eigenvalues with Symmetries / 240 \\
                 VIII.6 Problems / 244 \\
                 VIII.7 Notes and References / 249 \\
                 IX A Selection of Matrix Inequalities / 253 \\
                 IX.1 Some Basic Lemmas / 253 \\
                 IX.2 Products of Positive Matrices / 255 \\
                 IX.3 Inequalities for the Exponential Function / 258
                 \\
                 IX.4 Arithmetic-Geometric Mean Inequalities / 262 \\
                 IX.5 Schwarz Inequalities / 266 \\
                 IX.6 The Lieb Concavity Theorem / 271 \\
                 IX.7 Operator Approximation / 275 \\
                 IX.8 Problems / 279 \\
                 IX.9 Notes and References / 285 \\
                 X Perturbation of Matrix Functions / 289 \\
                 X.1 Operator Monotone Functions / 289 \\
                 X.2 The Absolute Value / 296 \\
                 X.3 Local Perturbation Bounds / 301 \\
                 X.4 Appendix: Differential Calculus / 310 \\
                 X.5 Problems / 317 \\
                 X.6 Notes and References / 320 \\
                 References / 325 \\
                 Index / 339",
}

@Book{Bhatia:2007:PDM,
  author =       "Rajendra Bhatia",
  title =        "Positive Definite Matrices",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "x + 254",
  year =         "2007",
  ISBN =         "0-691-12918-5",
  ISBN-13 =      "978-0-691-12918-1",
  LCCN =         "QA188 .B488 2007",
  MRclass =      "15-02 (15A48 42A82 43A35 47B65)",
  MRnumber =     "2284176 (2007k:15005)",
  MRreviewer =   "Ronald L. Smith",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Princeton Series in Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0713/2006050375-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0713/2006050375-t.html;
                 http://www.loc.gov/catdir/enhancements/fy0734/2006050375-b.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface / vii \\
                 1: Positive Matrices / 1 \\
                 1.1 Characterizations / 1 \\
                 1.2 Some Basic Theorems / 5 \\
                 1.3 Block Matrices / 12 \\
                 1.4 Norm of the Schur Product / 16 \\
                 1.5 Monotonicity and Convexity / 18 \\
                 1.6 Supplementary Results and Exercises / 23 \\
                 1.7 Notes and References / 29 \\
                 \\
                 2: Positive Linear Maps / 35 \\
                 2.1 Representations / 35 \\
                 2.2 Positive Maps / 36 \\
                 2.3 Some Basic Properties of Positive Maps / 38 \\
                 2.4 Some Applications / 43 \\
                 2.5 Three Questions / 46 \\
                 2.6 Positive Maps on Operator Systems / 49 \\
                 2.7 Supplementary Results and Exercises / 52 \\
                 2.8 Notes and References / 62 \\
                 \\
                 3: Completely Positive Maps / 65 \\
                 3.1 Some Basic Theorems / 66 \\
                 3.2 Exercises / 72 \\
                 3.3 Schwarz Inequalities / 73 \\
                 3.4 Positive Completions and Schur Products / 76 \\
                 3.5 The Numerical Radius / 81 \\
                 3.6 Supplementary Results and Exercises / 85 \\
                 3.7 Notes and References / 94 \\
                 \\
                 4: Matrix Means / 101 \\
                 4.1 The Harmonic Mean and the Geometric Mean / 103 \\
                 4.2 Some Monotonicity and Convexity Theorems / 111 \\
                 4.3 Some Inequalities for Quantum Entropy / 114 \\
                 4.4 Furuta's Inequality / 125 \\
                 4.5 Supplementary Results and Exercises / 129 \\
                 4.6 Notes and References / 136 \\
                 \\
                 5: Positive Definite Functions / 141 \\
                 5.1 Basic Properties / 141 \\
                 5.2 Examples / 144 \\
                 5.3 L{\"o}wner Matrices / 153 \\
                 5.4 Norm Inequalities for Means / 160 \\
                 5.5 Theorems of Herglotz and Bochner / 165 \\
                 5.6 Supplementary Results and Exercises / 175 \\
                 5.7 Notes and References / 191 \\
                 \\
                 6: Geometry of Positive Matrices / 201 \\
                 6.1 The Riemannian Metric / 201 \\
                 6.2 The Metric Space $\mathbb{P}_n$ / 210 \\
                 6.3 Center of Mass and Geometric Mean / 215 \\
                 6.4 Related Inequalities / 222 \\
                 6.5 Supplementary Results and Exercises / 225 \\
                 6.6 Notes and References / 232 \\
                 \\
                 Bibliography / 237 \\
                 Index / 247 \\
                 Notation 253",
}

@Book{Boas:1960:PRF,
  author =       "Ralph P. (Ralph Philip) Boas",
  title =        "A Primer of Real Functions",
  volume =       "13",
  publisher =    pub-MAA,
  address =      pub-MAA:adr,
  pages =        "xiii + 189",
  year =         "1960",
  LCCN =         "QA331 .B646",
  bibdate =      "Fri Nov 21 08:11:21 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "The Carus mathematical monographs",
  acknowledgement = ack-nhfb,
  author-dates = "1912--1992",
  subject =      "Functions of real variables",
}

@Book{Boas:1972:PRF,
  author =       "Ralph P. (Ralph Philip) Boas",
  title =        "A Primer of Real Functions",
  volume =       "13",
  publisher =    pub-MAA,
  address =      pub-MAA:adr,
  edition =      "Second",
  pages =        "xi + 196",
  year =         "1972",
  ISBN =         "0-88385-013-3",
  ISBN-13 =      "978-0-88385-013-8",
  LCCN =         "QA331.5 .B57 1972",
  bibdate =      "Fri Nov 21 08:11:21 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "The Carus mathematical monographs",
  acknowledgement = ack-nhfb,
  author-dates = "1912--1992",
  subject =      "Functions of real variables",
}

@Book{Boas:1981:PRF,
  author =       "Ralph P. (Ralph Philip) Boas",
  title =        "A Primer of Real Functions",
  volume =       "13",
  publisher =    pub-MAA,
  address =      pub-MAA:adr,
  edition =      "Third",
  pages =        "xi + 232",
  year =         "1981",
  ISBN =         "0-88385-022-2",
  ISBN-13 =      "978-0-88385-022-0",
  ISSN =         "0069-0813",
  LCCN =         "QA331.5 .B57 1981",
  bibdate =      "Fri Nov 21 08:15:05 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "The Carus mathematical monographs",
  URL =          "http://www.gbv.de/dms/bowker/toc/9780883850220.pdf",
  abstract =     "This is a revised, updated, and augmented edition of a
                 classic Carus monograph with a new chapter on
                 integration and its applications. Earlier editions
                 covered sets, metric spaces, continuous functions, and
                 differentiable functions. To that, this edition adds
                 sections on measurable sets and functions and the
                 Lebesgue and Stieltjes integrals. The book retains the
                 informal chatty style of the previous editions. It
                 presents a variety of interesting topics, many of which
                 are not commonly encountered in undergraduate
                 textbooks, such as the existence of continuous
                 everywhere-oscillating functions; two functions having
                 equal derivatives, yet not differing by a constant;
                 application of Stieltjes integration to the speed of
                 convergence of infinite series. For readers with a
                 background in calculus, the book is suitable either for
                 self-study or for supplemental reading in a course on
                 advanced calculus or real analysis. Students of
                 mathematics will find here the sense of wonder that was
                 associated with the subject in its early days.",
  acknowledgement = ack-nhfb,
  author-dates = "1912--1992",
  subject =      "Functions of real variables; Fonctions de variables
                 r{\'e}elles; Functions of real variables; Funktion
                 (Mathematik); Math{\'e}matiques; Funktion
                 (Mathematik)",
  tableofcontents = "I. Sets \\
                 1. Sets \\
                 2. Sets of real numbers \\
                 3. Countable and uncountable sets \\
                 4. Metric spaces \\
                 5. Open and closed sets \\
                 6. Dense and nowhere dense sets \\
                 7. Compactness \\
                 8. Convergence and completeness \\
                 9. Nested sets and Baire's theorem \\
                 10. Some applications of Baire's theorem \\
                 11. Sets of measure zero \\
                 II. Functions \\
                 12. Functions \\
                 13. Continuous functions \\
                 14. Properties of continuous functions \\
                 15. Upper and lower limits \\
                 16. Sequences of functions \\
                 17. Uniform convergence \\
                 18. Pointwise limits of continuous functions \\
                 19. Approximations to continuous functions \\
                 20. Linear functions \\
                 21. Derivatives \\
                 22. Monotonic functions \\
                 23. Convex functions \\
                 24. Infinitely differentiable functions",
  tableofcontents-2 = "Sets: \\
                 Sets \\
                 Sets of real numbers \\
                 Countable and uncountable sets \\
                 Metric spaces \\
                 Open and closed sets \\
                 Dense and nowhere dense sets \\
                 Compactness \\
                 Convergence and completeness \\
                 Nested sets and Baire's problem \\
                 Some applications of Baire's theorem \\
                 Sets of measure zero \\
                 Functions: \\
                 Functions \\
                 Continuous functions \\
                 Properties of continuous functions \\
                 Upper and lower limits \\
                 Sequences of functions \\
                 Uniform convergence \\
                 Pointwise limits of continuous functions \\
                 Approximations to continuous functions \\
                 Linear functions \\
                 Derivatives \\
                 Monotonic functions \\
                 Convex functions \\
                 Infinitely differentiable functions \\
                 Integration: \\
                 Lebesgue measure \\
                 Measurable functions \\
                 Definition of the Lebesgue integral \\
                 Properties of Lebesgue integrals \\
                 Applications of the Lebesgue integral \\
                 Stieltjes integrals \\
                 Applications of the Stieltjes integral \\
                 Partial sums of infinite series \\
                 Answers to exercises",
}

@Book{Boas:1996:PRF,
  author =       "Ralph P. (Ralph Philip) Boas",
  title =        "A Primer of Real Functions",
  volume =       "13",
  publisher =    pub-MAA,
  address =      pub-MAA:adr,
  edition =      "Fourth",
  pages =        "xiv + 305",
  year =         "1996",
  DOI =          "https://doi.org/10.5948/UPO9781614440130",
  ISBN =         "0-88385-029-X",
  ISBN-13 =      "978-0-88385-029-9",
  LCCN =         "QA331.5 .B57 1996",
  MRclass =      "26-01",
  MRnumber =     "1411907 (97f:26001)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Revised and with a preface by Harold P. Boas.",
  series =       "Carus Mathematical Monographs",
  URL =          "http://catdir.loc.gov/catdir/description/cam028/96077785.html;
                 http://catdir.loc.gov/catdir/toc/cam027/96077785.html",
  abstract =     "This is a revised, updated, and augmented edition of a
                 classic Carus monograph with a new chapter on
                 integration and its applications. Earlier editions
                 covered sets, metric spaces, continuous functions, and
                 differentiable functions. To that, this edition adds
                 sections on measurable sets and functions and the
                 Lebesgue and Stieltjes integrals. The book retains the
                 informal chatty style of the previous editions. It
                 presents a variety of interesting topics, many of which
                 are not commonly encountered in undergraduate
                 textbooks, such as the existence of continuous
                 everywhere-oscillating functions; two functions having
                 equal derivatives, yet not differing by a constant;
                 application of Stieltjes integration to the speed of
                 convergence of infinite series. For readers with a
                 background in calculus, the book is suitable either for
                 self-study or for supplemental reading in a course on
                 advanced calculus or real analysis. Students of
                 mathematics will find here the sense of wonder that was
                 associated with the subject in its early days.",
  acknowledgement = ack-nhfb,
  author-dates = "1912--1992",
  subject =      "Functions of real variables; Functions of real
                 variables; Re{\"e}le functies; Fonctions d'une variable
                 r{\'e}elle; Fonctions continues.",
  tableofcontents = "Preface to the fourth edition \\
                 Preface to the third edition \\
                 [ch.] 1. Sets \\
                 1. Sets \\
                 2. Sets of real numbers \\
                 3. Countable and uncountable sets \\
                 4. Metric spaces \\
                 5. Open and closed sets \\
                 6. Dense and nowhere dense sets \\
                 7. Compactness \\
                 8. Convergence and completeness \\
                 9. Nested sets and Baire's theorem \\
                 10. Some applications of Baire's theorem \\
                 11. Sets of measure zero \\
                 [ch.] 2. Functions \\
                 12. Functions \\
                 13. Continuous functions \\
                 14. Properties of continuous functions \\
                 15. Upper and lower limits \\
                 16. Sequences of functions \\
                 17. Uniform convergence \\
                 18. Point wise limits on continuous functions \\
                 19. Approximations to continuous functions \\
                 20. Linear functions \\
                 21. Derivatives \\
                 22. Monotonic functions \\
                 23. Convex functions \\
                 24. Infinitely differentiable functions \\
                 [ch.] 3. Integration \\
                 25. Lebesgue measure \\
                 26. Measurable functions \\
                 27. Definition of the Lebesgue integral \\
                 28. Properties of Lebesgue integrals \\
                 29. Applications of the Lebesgue integral \\
                 30. Stieltjes integrals \\
                 31. Applications of the Stieltjes integral \\
                 32. Partial sums of infinite series \\
                 Answers to exercises \\
                 Index",
}

@Book{Bonsall:1971:NRO,
  author =       "F. F. Bonsall and J. Duncan",
  title =        "Numerical Ranges of Operators on Normed Spaces and of
                 Elements of Normed Algebras",
  volume =       "2",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "iv + 142",
  year =         "1971",
  DOI =          "https://doi.org/10.1017/CBO9781107359895",
  ISBN =         "0-521-07988-8 (paperback), 1-107-35989-9 (e-book)",
  ISBN-13 =      "978-0-521-07988-4 (paperback), 978-1-107-35989-5
                 (e-book)",
  LCCN =         "QA322 .B65",
  MRclass =      "46.50 (47.00)",
  MRnumber =     "0288583 (44 \#5779)",
  MRreviewer =   "T. W. Palmer",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "London Mathematical Society Lecture Note Series",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0808/71128498-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0808/71128498-t.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  remark =       "Continued by \cite{Bonsall:1973:NRI}.",
  subject =      "Normed linear spaces; Banach algebras; Linear
                 operators",
  tableofcontents = "1. Numerical range in unital normed algebras \\
                 2. Hermitian elements of a complex unital Banach
                 algebra \\
                 3. Operators \\
                 4. Some recent developments",
}

@Book{Bonsall:1973:NRI,
  author =       "F. F. Bonsall and J. Duncan",
  title =        "Numerical Ranges. {II}",
  volume =       "10",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "vii + 179",
  year =         "1973",
  DOI =          "https://doi.org/10.1017/CBO9780511662515",
  ISBN =         "0-521-20227-2 (paperback), 0-511-66251-3 (e-book)",
  ISBN-13 =      "978-0-521-20227-5 (paperback), 978-0-511-66251-5
                 (e-book)",
  LCCN =         "QA322.2 .B66",
  MRclass =      "46H05 (46K05 47A10)",
  MRnumber =     "0442682 (56 \#1063)",
  MRreviewer =   "T. W. Palmer",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "London Mathematical Society Lecture Notes",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0827/73179782-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0827/73179782-t.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  remark =       "Continuation of \cite{Bonsall:1971:NRO}.",
  subject =      "Normed linear spaces; Banach algebras; Linear
                 operators",
  tableofcontents = "5. Spatial numerical ranges \\
                 6. Algebra numerical ranges \\
                 7. Further ranges",
}

@Book{Bowman:1962:IDMa,
  author =       "Frank Bowman",
  title =        "An Introduction to Determinants and Matrices:
                 Determinants and Matrices",
  publisher =    "Van Nostrand",
  address =      "Princeton, NJ, USA",
  pages =        "163",
  year =         "1962",
  LCCN =         "QA191",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Applied mathematics series",
  acknowledgement = ack-nhfb,
  author-dates = "1891--",
  subject =      "Determinants; Matrices",
}

@Book{Bowman:1962:IDMb,
  author =       "Frank Bowman",
  title =        "An Introduction to Determinants and Matrices:
                 Determinants and Matrices",
  publisher =    "English Universities Press",
  address =      "London, UK",
  pages =        "ix + 163",
  year =         "1962",
  LCCN =         "QA191 .B6",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Applied mathematics series",
  acknowledgement = ack-nhfb,
  author-dates = "1891--",
  subject =      "Determinants; Matrices",
}

@Book{Browne:1958:ITD,
  author =       "Edward Tankard Browne",
  title =        "Introduction to the Theory of Determinants and
                 Matrices",
  publisher =    pub-U-NC,
  address =      pub-U-NC:adr,
  pages =        "270",
  year =         "1958",
  LCCN =         "QA263 .B7",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1959",
  subject =      "Matrices; Determinants",
}

@Book{Brualdi:1991:CMT,
  author =       "Richard A. Brualdi and Herbert J. Ryser",
  title =        "Combinatorial Matrix Theory",
  volume =       "39",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 367",
  year =         "1991",
  DOI =          "https://doi.org/10.1017/CBO9781107325708",
  ISBN =         "0-521-32265-0",
  ISBN-13 =      "978-0-521-32265-2",
  LCCN =         "QA188 .B78 1991",
  MRclass =      "05C50 (05B15 05B20)",
  MRnumber =     "1130611 (93a:05087)",
  MRreviewer =   "S. K. Tharthare",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Encyclopedia of Mathematics and its Applications",
  URL =          "http://www.loc.gov/catdir/description/cam024/90020210.html;
                 http://www.loc.gov/catdir/toc/cam024/90020210.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Matrices; Combinatorial analysis",
  tableofcontents = "1. Incidence matrices \\
                 2. Matrices and graphs \\
                 3. Matrices and digraphs \\
                 4. Matrices and bigraphs \\
                 5. Combinatorial matrix algebra \\
                 6. Existence theorems for combinatorially constrained
                 matrices \\
                 7. Some special graphs \\
                 8. The permanent \\
                 9. Latin squares",
}

@Book{Brualdi:1995:MSS,
  author =       "Richard A. Brualdi and Bryan L. Shader",
  title =        "Matrices of Sign-Solvable Linear Systems",
  volume =       "116",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xii + 298",
  year =         "1995",
  DOI =          "https://doi.org/10.1017/CBO9780511574733",
  ISBN =         "0-521-48296-8",
  ISBN-13 =      "978-0-521-48296-7",
  LCCN =         "QA188 .B79 1995",
  MRclass =      "15-02 (90A14 90C08)",
  MRnumber =     "1358133 (97k:15001)",
  MRreviewer =   "Gerard Sierksma",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Cambridge Tracts in Mathematics",
  URL =          "http://www.loc.gov/catdir/description/cam026/94040931.html;
                 http://www.loc.gov/catdir/toc/cam024/94040931.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "1. Sign-solvability \\
                 2. $L$-matrices \\
                 3. Sign-solvability and digraphs \\
                 4. $S$-matrices \\
                 5. Beyond $S*$-matrices \\
                 6. $SNS$-matrices \\
                 7. $S2NS$-matrices \\
                 8. External properties of $L$-Matrices \\
                 9. The inverse sign pattern graph \\
                 10. Sign stability \\
                 11. Related topics",
}

@Book{Campbell:1979:GIL,
  author =       "S. L. (Stephen La Vern) Campbell and C. D. (Carl Dean)
                 {Meyer, Jr.}",
  title =        "Generalized Inverses of Linear Transformations",
  publisher =    pub-PITMAN,
  address =      pub-PITMAN:adr,
  pages =        "xi + 272",
  year =         "1979",
  ISBN =         "0-273-08422-4",
  ISBN-13 =      "978-0-273-08422-8",
  LCCN =         "QA188 .C36",
  bibdate =      "Fri Nov 21 08:24:15 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Reprinted in \cite{Campbell:1991:GIL}.",
  series =       "Surveys and reference works in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Matrix inversion; Transformations (Mathematics)",
  tableofcontents = "Preface / vii \\
                 0 Introduction and other preliminaries I Prerequisites
                 and philosophy / 1 \\
                 2 Notation and basic geometry / 2 \\
                 3 Exercises / 6 \\
                 The Moore--Penrose or generalized inverse / 8 \\
                 1 Basic definitions / 8 \\
                 2 Basic properties of the generalized inverse / 10 \\
                 3 Computation of $A^\dagger$ / 12 \\
                 4 Generalized inverse of a product / 19 \\
                 5 Exercises / 25 \\
                 2 Least squares solutions / 28 \\
                 1 What kind of answer is $A^\dagger b$'? / 28 \\
                 2 Fitting a linear hypothesis / 30 \\
                 3 Estimating the unknown parameters / 32 \\
                 4 Goodness of fit / 34 \\
                 5 An application to curve fitting / 39 \\
                 6 Polynomial and more general fittings / 42 \\
                 7 Why $A^\dagger$? / 45 \\
                 3 Sums, partitioned matrices and the constrained
                 generalized inverse / 46 \\
                 1 The generalized inverse of a sum / 46 \\
                 2 Modified matrices / 51 \\
                 3 Partitioned. matrices / 53 \\
                 4 Block triangular matrices / 61 \\
                 5 The fundamental matrix of constrained minimization /
                 63 \\
                 6 Constrained least squares and constrained generalized
                 inverses / 65 \\
                 7 Exercises / 69 \\
                 4 Partial isometries and EP matrices / 71 \\
                 1 Introduction / 71 \\
                 2 Partial isometries / 71 \\
                 3 EP matrices / 74 \\
                 4 Exercises / 75 \\
                 5 The generalized inverse in electrical engineering /
                 77 \\
                 1 Introduction / 77 \\
                 2 $n$-port networks and the impedance matrix / 77 \\
                 3 Parallel sums / 82 \\
                 4 Shorted matrices / 86 \\
                 5 Other uses of the generalized inverse / 88 \\
                 6 Exercises / 88 \\
                 7 References and further reading / 89 \\
                 6 $(i,j,k)$-Generalized inverses and linear estimation
                 / 91 \\
                 1 Introduction / 91 \\
                 2 Definitions / 91 \\
                 3 $(l)$-inverses / 96 \\
                 4 Applications to the theory of linear estimation / 104
                 \\
                 5 Exercises / 115 \\
                 7 The Orazio inverse / 120 \\
                 1 Introduction / 120 \\
                 2 Definitions / 121 \\
                 3 Basic properties of the Drazin inverse / 127 \\
                 4 Spectral properties of the Drazin inverse / 129 \\
                 5 $A^D$ as a polynomial in $A$ / 130 \\
                 6 $A^D$ as a limit / 136 \\
                 7 The Drazin inverse of a partitioned matrix / 139 \\
                 8 Other properties / 147 \\
                 8 Applications of the Orazio inverse to the theory of
                 finite Markov chains / 151 \\
                 1 Introduction and terminology / 151 \\
                 2 Introduction of the Drazin inverse into the theory of
                 finite Markov chains / 152 \\
                 3 Regular chains / 157 \\
                 4 Ergodic chains / 158 \\
                 5 Calculation of $A^\#$ and $w^*$ for an ergodic chain
                 / 160 \\
                 6 Non-ergodic chains and absorbing chains / 165 \\
                 7 References and further reading / 170 \\
                 9 Applications of the Orazio inverse / 171 \\
                 1 Introduction / 171 \\
                 2 Applications of the Drazin inverse to linear systems
                 of differential equations / 171 \\
                 3 Applications of the Drazin inverse to difference
                 equations / 181 \\
                 4 The Leslie population growth model and backward
                 population projection / 184 \\
                 5 Optimal control / 187 \\
                 6 Functions of a matrix / 200 \\
                 7 Weak Drazin inverses / 202 \\
                 8 Exercises / 208 \\
                 10 Continuity of the generalized inverse / 210 \\
                 I Introduction / 210 \\
                 2 Matrix norms / 210 \\
                 3 Matrix norms and invertibility / 214 \\
                 4 Continuity of the Moore--Penrose generalized inverse
                 / 216 \\
                 5 Matrix valued functions / 224 \\
                 6 Non-linear least squares problems: an example / 229
                 \\
                 7 Other inverses / 231 \\
                 8 Exercises / 234 \\
                 9 References and further reading / 235 \\
                 11 Linear programming / 236 \\
                 1 Introduction and basic theory / 236 \\
                 2 Pyle's reformulation / 241 \\
                 3 Exercises / 244 \\
                 4 References and further reading / 245 \\
                 12 Computational concerns / 246 \\
                 1 Introduction / 246 \\
                 2 Calculation of $A^\dagger$ / 247 \\
                 3 Computation of the singular value decomposition / 251
                 \\
                 4 $(l)$-inverses / 255 \\
                 5 Computation of the Drazin inverse / 255 \\
                 6 Previous algorithms / 260 \\
                 7 Exercises / 261 \\
                 Bibliography / 263 \\
                 Index 269",
}

@Book{Campbell:1991:GIL,
  author =       "S. L. (Stephen La Vern) Campbell and C. D. (Carl Dean)
                 {Meyer, Jr.}",
  title =        "Generalized Inverses of Linear Transformations",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 272",
  year =         "1991",
  ISBN =         "0-486-66693-X (paperback)",
  ISBN-13 =      "978-0-486-66693-8 (paperback)",
  LCCN =         "QA188 .C36 1991",
  bibdate =      "Fri Nov 21 08:24:15 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/90023852.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  remark =       "Reprint, with corrections. Originally published:
                 London; San Francisco: Pitman, 1979, in series: Surveys
                 and reference works in mathematics.",
  subject =      "Matrix inversion; Transformations (Mathematics)",
}

@Book{Campbell:2009:GIL,
  author =       "S. L. (Stephen La Vern) Campbell and C. D. (Carl Dean)
                 {Meyer, Jr.}",
  title =        "Generalized Inverses of Linear Transformations",
  volume =       "56",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xx + 272",
  year =         "2009",
  DOI =          "https://doi.org/10.1137/1.9780898719048",
  ISBN =         "0-89871-671-3, 0-89871-904-6 (e-book)",
  ISBN-13 =      "978-0-89871-671-9, 978-0-89871-904-8 (e-book)",
  LCCN =         "QA188 .C36 2009",
  bibdate =      "Fri Nov 21 08:24:15 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Classics in applied mathematics",
  URL =          "http://epubs.siam.org/ebooks/siam/classics_in_applied_mathematics/cl56;
                 http://www.loc.gov/catdir/enhancements/fy0916/2008046428-b.html;
                 http://www.loc.gov/catdir/enhancements/fy0916/2008046428-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0916/2008046428-t.html",
  abstract =     "Generalized (or pseudo-) inverse concepts routinely
                 appear throughout applied mathematics and engineering,
                 in both research literature and textbooks. Although the
                 basic properties are readily available, some of the
                 more subtle aspects and difficult details of the
                 subject are not well documented or understood. First
                 published in 1979, \booktitle{Generalized Inverses of
                 Linear Transformations} remains up-to-date and
                 readable, and it includes chapters on Markov chains and
                 the Drazin inverse methods that have become significant
                 to many problems in applied mathematics. The book
                 provides comprehensive coverage of the mathematical
                 theory of generalized inverses coupled with a wide
                 range of important and practical applications that
                 includes topics in electrical and computer engineering,
                 control and optimization, computing and numerical
                 analysis, statistical estimation, and stochastic
                 processes. Audience: intended for use as a reference by
                 applied scientists and engineers.",
  acknowledgement = ack-nhfb,
  remark =       "Originally published: London: Pitman Pub., 1979.",
  subject =      "Matrix inversion; Transformations (Mathematics);
                 Matrix inversion.; Transformations (Mathematics)",
  tableofcontents = "Introduction and other preliminaries \\
                 The Moore--Penrose or generalized inverse \\
                 Least squares solutions \\
                 Sums, partitioned matrices and the constrained
                 generalized inverse \\
                 Partial isometries and EP matrices \\
                 The generalized inverse in electrical engineering \\
                 $(i, j, k)$-Generalized inverses and linear estimation
                 \\
                 The Drazin inverse \\
                 Applications of the Drazin inverse to the theory of
                 finite Markov chains \\
                 Applications of the Drazin inverse \\
                 Continuity of the generalized inverse \\
                 Linear programming \\
                 Computational concerns",
}

@Book{Carlson:2002:LAG,
  editor =       "David (David H.) Carlson and others",
  title =        "Linear Algebra Gems: Assets for Undergraduate
                 Mathematics",
  volume =       "59",
  publisher =    pub-MAA,
  address =      pub-MAA:adr,
  pages =        "xvi + 328",
  year =         "2002",
  ISBN =         "0-88385-170-9 (paperback)",
  ISBN-13 =      "978-0-88385-170-8 (paperback)",
  LCCN =         "QA184.2 .L55 2002",
  bibdate =      "Fri Nov 21 08:27:10 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "MAA notes",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Algebras, Linear; Alg{\`e}bre lin{\'e}aire; Lineare
                 Algebra; Algebras, Linear",
  tableofcontents = "Part 1: Partitioned matrix multiplication \\
                 Introduction / Editors \\
                 Modern views of matrix multiplication / Editors \\
                 The associativity of matrix multiplication / Editors
                 \\
                 Relationships between $A B$ and $B A$ / Editors \\
                 The characteristic polynomial of a partitioned matrix /
                 D. Steven Mackey \\
                 The Cauchy--Binet formula / Wayne Barrett \\
                 Cramer's rule / Editors \\
                 The multiplicativity of the determinant / William
                 Watkins and the editors \\
                 Part 2: Determinants \\
                 Introduction / Editors \\
                 The determinant of a sum of matrices / L. M. Weiner \\
                 Determinants of sums / Marvin Marcus \\
                 An application of determinants / Helen Skala \\
                 Cramer's rule via selective annihilation / Dan Kalman
                 \\
                 The multiplication of determinants / D. C. Lewis \\
                 A short proof of a result of determinants / George
                 Marsaglia \\
                 Dodgson's identity / Wayne Barrett \\
                 On the evaluation of determinants by Chi{\`o}'s method
                 / L. E. Fuller, J. D. Logan \\
                 Apropos predetermined determinants / Antal E. Fekete
                 \\
                 Part 3: Eigenanalysis \\
                 Introduction / Editors \\
                 Eigenvalues, eigenvectors and linear matrix equations /
                 Charles R. Johnson \\
                 Matrices with integer entries and integer eigenvalues /
                 J. C. Renaud \\
                 Matrices with ``custom built'' eigenspaces / W. P.
                 Galvin \\
                 A note on normal matrices / C. G. Cullen \\
                 Eigenvectors: fixed vectors and fixed directions
                 (discovery exercises) / J. Stuart \\
                 On Cauchy's inequalities for Hermitian matrices /
                 Emeric Deutsch, Harry Hochstadt \\
                 The monotonicity theorem, Cauchy's interlace theorem
                 and the Courant--Fisher theorem / Yasuhiko Ikebe, [et
                 al.]\ldots{} \\
                 The power method for finding eigenvalues on a
                 microcomputer / Gareth Williams, Donna Williams \\
                 Singular values and the spectral theorem / K.
                 Hoechsmann \\
                 The characteristic polynomial of singular matrix / D.
                 E. Varberg \\
                 Characteristic roots of rank $1$ matrices / Larry
                 Cummings \\
                 A method for finding the eigenvectors of an $n \times
                 n$ matrix corresponding to eigenvalues of multiplicity
                 one / M. Carchidi \\
                 Part 4: Geometry \\
                 Introduction / Editors \\
                 Gram--Schmidt projections / Charles R. Johnson, D.
                 Olesky, P. van den Driessche \\
                 Pythagoras and the Cauchy--Schwarz inequality / Ladnor
                 Geissinger \\
                 An application of the Schwarz inequality / V. G.
                 Sigillito \\
                 A geometric interpretation of Cramer's rule / Gregory
                 Conner, Michael Lundquist \\
                 Isometries of $L_p$-norm / Chi-Kwong Li, Wasin So \\
                 Matrices which take a given vector into a given vector
                 / M. Machover \\
                 The matrix of a rotation / Roger C. Alperin \\
                 Standard least squares problem / James Foster \\
                 Multigrid graph paper / Jean H. Bevis \\
                 Part 5: Matrix forms \\
                 Introduction / Editors \\
                 LU factorization / Charles R. Johnson \\
                 Singular value decomposition: the $2 \times 2$ case /
                 Michael Lundquist \\
                 A simple proof of the Jordan decomposition theorem for
                 matrices / Israel Gohberg and Seymour Goldberg \\
                 Similarity of matrices / William Watkins \\
                 Classifying row-reduced echelon matrices / Stewart
                 Venit, Wayne Bishop \\
                 Part 6: Polynomials and matrices \\
                 Introduction / Editors \\
                 On the Cayley--Hamilton theorem / Robert Reams \\
                 On polynomial matrix equations / Harley Flanders \\
                 The matrix equation $X^2 = A$ / W. R. Utz \\
                 Where did the variables go? / Stephen Barnett \\
                 A zero-row reduction algorithm for obtaining the gcd of
                 polynomials / Sidney H. Kung, Yap S. Chua \\
                 Part 7: Linear systems, inverses, and rank \\
                 Introduction / Editors \\
                 Left and right inverses / Editors \\
                 row and column ranks are always equal / Dave Stanford
                 \\
                 A proof of the equality of column and row rank of a
                 matrix / Hans Liebeck \\
                 The Frobenius rank inequality / Donald Robinson \\
                 A new algorithm for computing the rank of a matrix /
                 Larry Gerstein \\
                 Elementary row operations and LU decomposition / David
                 P. Kraines, Vivian Krains, David A. Smith \\
                 A succinct notation for linear combinations of abstract
                 vectors / Leon Katz \\
                 Why should we pivot in Gaussian elimination? / Edward
                 Rozema \\
                 The Gaussian algorithm for linear systems with interval
                 data / G. Alefeld, G. Mayer \\
                 On Sylvester's law of nullity / Kurt Bing \\
                 Inverses of Vandermonde Matrices / F. D. Parker \\
                 On one-sided inverses of matrices / Elmar Zemgalis \\
                 Integer matrices whose inverses contain only integers /
                 Robert Hanson \\
                 Part 8: Applications \\
                 Introduction / Editors \\
                 The matrix-tree theorem / Ralph P. Grimaldi, Robert J.
                 Lopez \\
                 Algebraic integers and tensor products of matrices /
                 Shaun M. Fallat \\
                 On regular Markov chains / Nicholas J. Rose \\
                 Integration by matrix inversion / William Swartz \\
                 Some explicit formulas for the exponential matrix / T.
                 M. Apostol \\
                 Avoiding the Jordan canonical form in the discussion of
                 linear systems with constant coefficients / E. J.
                 Putzer \\
                 The discrete analogue of the Putzer algorithm / Saber
                 Elaydi \\
                 The minimum length of a permutation as a product of
                 transpositions / George Mackiw \\
                 Part 9: Problems \\
                 Introduction / Editors \\
                 Partitioned matrix multiplication \\
                 Determinants \\
                 Eigenanalysis \\
                 Geometry \\
                 Matrix forms \\
                 Matrix equations \\
                 Linear systems, inverses, and rank \\
                 Applications \\
                 Hermitian matrices \\
                 Magic squares \\
                 Special matrices \\
                 Stochastic matrices \\
                 Trace \\
                 Other topics",
}

@Book{Chatelin:1993:EM,
  author =       "Fran{\c{c}}oise Chatelin",
  title =        "Eigenvalues of Matrices",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xviii + 382",
  year =         "1993",
  ISBN =         "0-471-93538-7",
  ISBN-13 =      "978-0-471-93538-4",
  LCCN =         "QA188 .C44 1993",
  MRclass =      "65-01 (15A18 65F15 65F50)",
  MRnumber =     "1232655 (94d:65002)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "With exercises by Mario Ahu{\'e}s and the author,
                 Translated from the French and with additional material
                 by Walter Ledermann",
  series =       "Pure and applied mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0707/93003430-d.html;
                 http://www.loc.gov/catdir/toc/onix04/93003430.html",
  acknowledgement = ack-nhfb # " and " # ack-rah,
  subject =      "Matrices; Eigenvalues",
  tableofcontents = "Preface / xi \\
                 Preface to the English Edition / xv \\
                 Notation / xvii \\
                 1: Supplements from Linear Algebra / 1 \\
                 1.1 Notation and definitions / 1 \\
                 1.2 The canonical angles between two subspaces / 5 \\
                 1.3 Projections / 8 \\
                 1.4 The gap between two subspaces / 10 \\
                 1.5 Convergence of a sequence of subspaces / 14 \\
                 1.6 Reduction of Square matrices / 18 \\
                 1.7 Spectral decomposition / 27 \\
                 1.8 Rank and linear independence / 31 \\
                 1.9 Hermitian and normal matrices / 32 \\
                 1.10 Non-negative matrices / 33 \\
                 1.11 Sections and Rayleigh quotients / 34 \\
                 1.12 Sylvester's equation / 35 \\
                 1.13 Regular pencils of matrices / 42 \\
                 1.14 Bibliographical comments / 43 \\
                 Exercises / 43 \\
                 2: Elements of Spectral Theory / 61 \\
                 2.1 Revision of some properties of functions of a
                 complex variable / 61 \\
                 2.2 Singularities of the resolvent / 63 \\
                 2.3 The reduced resolvent and the partial inverse / 73
                 \\
                 2.4 The block-reduced resolvent / 76 \\
                 2.5 Linear perturbations of the matrix A / 79 \\
                 2.6 Analyticity of the resolvent / 82 \\
                 2.7 Analyticity of the spectral projection / 84 \\
                 2.8 The Rellich--Kato expansions / 85 \\
                 2.9 The Rayleigh--Schr{\"o}dinger expansions / 86 \\
                 2.10 Non-linear equation and Newton's method / 89 \\
                 2.11 Modified methods / 92 \\
                 2.12 The local approximate inverse and the method of
                 residual correction / 95 \\
                 2.13 Bibliographical comments / 98 \\
                 Exercises / 98 \\
                 3: Why Compute Eigenvalues? / 111 \\
                 3.1 Differential equations and difference equations /
                 111 \\
                 3.2 Markov chains / 114 \\
                 3.3 Theory of economics / 117 \\
                 3.4 Factorial analysis of data / 119 \\
                 3.5 The dynamics of structures / 120 \\
                 3.6 Chemistry / 122 \\
                 3.7 Fredholm's integral equation / 124 \\
                 3.8 Bibliographical comments / 126 \\
                 Exercises / 126 \\
                 4: Error Analysis / 149 \\
                 4.1 Revision of the conditioning of a System / 149 \\
                 4.2 Stability of a spectral problem / 150 \\
                 4.3 A priori analysis of errors / 165 \\
                 4.4 A posteriori analysis of errors / 170 \\
                 4.5 A is almost diagonal / 177 \\
                 4.6 A is Hermitian / 180 \\
                 4.7 Bibliographical comments / 190 \\
                 Exercises / 191 \\
                 5: Foundations of Methods for Computing Eigenvalues /
                 205 \\
                 5.1 Convergence of a Krylov sequence of subspaces / 205
                 \\
                 5.2 The method of subspace iteration / 208 \\
                 5.3 The power method / 213 \\
                 5.4 The method of inverse iteration / 217 \\
                 5.5 The $Q R$ algorithm / 221 \\
                 5.6 Hermitian matrices / 226 \\
                 5.7 The $Q Z$ algorithm / 226 \\
                 5.8 Newton's method and the Rayleigh quotient iteration
                 / 227 \\
                 5.9 Modified Newton's method and simultaneous inverse
                 iterations / 228 \\
                 5.10 Bibliographical comments / 235 \\
                 Exercises / 235 \\
                 6: Numerical Methods for Large Matrices / 251 \\
                 6.1 The principle of the methods / 251 \\
                 6.2 The method of subspace iteration revisited / 253
                 \\
                 6.3 The Lanczos method / 257 \\
                 6.4 The block Lanczos method / 266 \\
                 6.5 The generalized problem $K x = I M x$ / 270 \\
                 6.6 Arnoldi's method / 272 \\
                 6.7 Oblique projections / 279 \\
                 6.8 Bibliographical comments / 280 \\
                 Exercises / 281 \\
                 7: Chebyshev's Iterative Methods / 293 \\
                 7.1 Elements of the theory of uniform approximation for
                 a compact set in C / 293 \\
                 7.2 Chebyshev polynomials of a real variable / 299 \\
                 7.3 Chebyshev polynomials of a complex variable / 300
                 \\
                 7.4 The Chebyshev acceleration for the power method /
                 304 \\
                 7.5 The Chebyshev iteration method / 305 \\
                 7.6 Simultaneous Chebyshev iterations (with projection)
                 / 308 \\
                 7.7 Determination of the optimal parameters / 311 \\
                 7.8 Least Squares polynomials on a polygon / 312 \\
                 7.9 The hybrid methods of Saad / 314 \\
                 7.10 Bibliographical comments / 316 \\
                 Exercises / 316 \\
                 Appendices / 323 \\
                 A Solution to Exercises / 323 \\
                 B References for Exercises / 367 \\
                 C References / 371 \\
                 Index / 378",
}

@Book{Childs:1979:CIH,
  author =       "Lindsay N. Childs",
  title =        "A Concrete Introduction to Higher Algebra",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 338",
  year =         "1979",
  ISBN =         "0-387-90333-X (New York), 3-540-90333-X (Berlin)",
  ISBN-13 =      "978-0-387-90333-0 (New York), 978-3-540-90333-8
                 (Berlin)",
  LCCN =         "QA155 .C53",
  MRclass =      "00A05",
  MRnumber =     "520728 (80b:00001)",
  MRreviewer =   "Paul Jambor",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Undergraduate Texts in Mathematics",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Part I Integers \\
                 1: Numbers / 3 \\
                 2: Induction; the Binomial Theorem / 7 \\
                 A. Induction / 7 \\
                 B. Another Form of Induction / 11 \\
                 C. Well-ordering / 13 \\
                 D. The Binomial Theorem / 14 \\
                 3: Unique Factorization into Products of Primes / 19
                 \\
                 A. Euclid's Algorithm / 19 \\
                 B. Greatest Common Divisors / 22 \\
                 C. Unique Factorization / 26 \\
                 D. Exponential Notation; Least Common Multiples / 28
                 \\
                 4: Primes / 31 \\
                 A. Euclid / 31 \\
                 B. Some Analytic Results / 32 \\
                 C. The Prime Number Theorem / 35 \\
                 5: Bases / 37 \\
                 A. Numbers in Base a / 37 \\
                 B. Operations in Base a / 39 \\
                 C. Multiple Precision Long Division / 41 \\
                 D. Decimal Expansions / 44 \\
                 6: Congruences / 47 \\
                 A. Definition of Congruence / 47 \\
                 B. Basic Properties / 48 \\
                 C. Divisibility Tricks / 49 \\
                 D. More Properties of Congruence / 51 \\
                 E. Congruence Problems / 52 \\
                 F. Round Robin Tournaments / 54 \\
                 7: Congruence Classes / 56 \\
                 8: Rings and Fields / 62 \\
                 A. Axioms / 62 \\
                 B. lm / 65 \\
                 9: Matrices and Vectors / 68 \\
                 A. Matrix Multiplication / 68 \\
                 B. The Ring of n X n Matrices / 70 \\
                 C. Linear Equations / 73 \\
                 D. Determinants and Inverses / 75 \\
                 E. Row Operations / 76 \\
                 F. Subspaces, Bases, Dimension / 80 \\
                 10: Secret Codes, I / 84 \\
                 11: Fermat's Theorem, I: Abelian Groups / 90 \\
                 A. Fermat's Theorem / 90 \\
                 B. Abelian Groups / 91 \\
                 C. Euler's Theorem / 94 \\
                 D. Finding High Powers mod m / 95 \\
                 E. The Order of an Element / 96 \\
                 F. About Finite Fields / 97 \\
                 G. Nonabelian Groups / 98 \\
                 12: Repeating Decimals, I JOI Chapter 13: Error
                 Correcting Codes, I / 105 \\
                 14: The Chinese Remainder Theorem / 112 \\
                 A. The Theorem / 112 \\
                 B. A Generalization of Fermat's Theorem / 116 \\
                 15: Secret Codes, II / 118 \\
                 Part II Polynomials / 123 \\
                 1: Polynomials / 125 \\
                 2: Unique Factorization / 129 \\
                 A. Division Theorem / 129 \\
                 B. Greatest Common Divisors / 132 \\
                 C. Factorization into Irreducible Polynomials / 134 \\
                 3: The Fundamental Theorem of Algebra / 136 \\
                 A. Irreducible Polynomials in C[x] / 136 \\
                 B. Proof of the Fundamental Theorem / 138 \\
                 4: Irreducible Polynomials in IR[x] / 142 \\
                 5: Partial Fractions / 144 \\
                 A. Rational Functions / 144 \\
                 B. Partial Fractions / 145 \\
                 C. Integrating / 148 \\
                 D. A Partitioning Formula / 151 \\
                 6: The Derivative of a Polynomial / 157 \\
                 7: Sturm's Algorithm / 160 \\
                 8: Factoring in Q[ x ], I / 166 \\
                 A. Gauss's Lemma / 166 \\
                 B. Finding Roots / 168 \\
                 C. Testing for Irreducibility / 169 \\
                 9: Congruences Modulo a Polynomial / 173 \\
                 10: Fermat's Theorem, II / 175 \\
                 A. The Characteristic of a Field / 175 \\
                 B. Applications of the Binomial Theorem / 176 \\
                 11: Factoring in Q[x], II: Lagrange Interpolation / 180
                 \\
                 A. The Chinese Remainder Theorem / 180 \\
                 B. The Method of Lagrange Interpolation / 181 \\
                 12: Factoring in Zp[x] / 185 \\
                 13: Factoring in Q[x], III: Mod m / 193 \\
                 A. Bounding the Coefficients of Factors of a Polynomial
                 / 194 \\
                 B. Factoring Modulo High Powers of Primes / 198 \\
                 Part III Fields / 205 \\
                 1: Primitive Elements / 207 \\
                 2: Repeating Decimals, II / 212 \\
                 3: Testing for Primeness / 218 \\
                 4: Fourth Roots of One in ZP / 222 \\
                 A. Primes / 222 \\
                 B. Finite Fields of Complex Numbers / 223 \\
                 5: Telephone Cable Splicing / 226 \\
                 6: Factoring in Q[x], IV: Bad Examples Modp / 229 \\
                 7: Congruence Classes Modulo a Polynomial: Simple Field
                 Extensions / 231 \\
                 8: Polynomials and Roots / 237 \\
                 A. Inventing Roots of Polynomials / 237 \\
                 B. Finding Polynomials with Given Roots / 238 \\
                 9: Error Correcting Codes, II / 242 \\
                 10: Isomorphisms, I / 255 \\
                 A. Definitions / 255 \\
                 B. Examples Involving $\mathbb{Z}$ / 257 \\
                 C. Examples Involving $F[x]$ / 259 \\
                 D. Automorphisms / 261 \\
                 11: Finite Fields are Simple / 264 \\
                 12: Latin Squares / 267 \\
                 13: Irreducible Polynomials in $\mathbb{Z}_p[x]$ / 273
                 \\
                 A. Factoring $x^{p^*} - x$ / 273 \\
                 B. Counting Irreducible Polynomials / 275 \\
                 14: Finite Fields / 280 \\
                 15: The Discriminant and Stickelberger's Theorem / 282
                 \\
                 A. The Discriminant / 282 \\
                 B. Roots of Irreducible Polynomials in
                 $\mathbb{Z}_p[x]$ / 287 \\
                 C. Stickelberger's Theorem / 288 \\
                 16: Quadratic Residues / 291 \\
                 A. Reduction to the Odd Prime Case / 291 \\
                 B. The Legendre Symbol / 293 \\
                 C. Proof of the Law of Quadratic Reciprocity / 296 \\
                 17: Duplicate Bridge Tournaments / 300 \\
                 A. Hadamard Matrices / 300 \\
                 B. Duplicate Bridge Tournaments / 302 \\
                 C. Bridge for $8$ / 303 \\
                 D. Bridge for $p + 1$ / 306 \\
                 18: Algebraic Number Fields / 309 \\
                 19: Isomorphisms, II / 314 \\
                 20: Sums of Two Squares / 316 \\
                 21: On Unique Factorization / 320 \\
                 Exercises Used in Subsequent Chapters / 323 \\
                 Comments on the Starred Problems / 325 \\
                 References / 332 \\
                 Index / 335",
}

@Book{Childs:1995:CIH,
  author =       "Lindsay N. Childs",
  title =        "A Concrete Introduction to Higher Algebra",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xv + 522",
  year =         "1995",
  DOI =          "https://doi.org/10.1007/978-1-4419-8702-0",
  ISBN =         "0-387-94484-2 (hardcover), 1-4419-8702-9 (e-book)",
  ISBN-13 =      "978-0-387-94484-5 (hardcover), 978-1-4419-8702-0
                 (e-book)",
  LCCN =         "QA155 .C53 1995",
  bibdate =      "Fri Nov 21 14:16:31 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Undergraduate texts in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Algebra",
  tableofcontents = "Introduction / vii \\
                 1: Numbers / 1 \\
                 2: Induction / 8 \\
                 A. Induction / 8 \\
                 B. Another Form of Induction / 13 \\
                 C. Well-Ordering / 16 \\
                 D. Division Theorem / 18 \\
                 E. Bases / 20 \\
                 F. Operations in Base $a$ / 23 \\
                 3: Euclid's Algorithm / 25 \\
                 A. Greatest Common Divisors / 25 \\
                 B. Euclid's Algorithm / 27 \\
                 C. B{\'e}zout's Identity / 29 \\
                 D. The Efficiency of Euclid's Algorithm / 36 \\
                 E. Euclid's Algorithm and Incommensurability / 40 \\
                 4: Unique Factorization / 47 \\
                 A. The Fundamental Theorem of Arithmetic / 47 \\
                 B. Exponential Notation / 50 \\
                 C. Primes / 55 \\
                 D. Primes in an Interval / 59 \\
                 5: Congruences / 63 \\
                 A. Congruence Modulo $m$ / 63 \\
                 B. Basic Properties / 65 \\
                 C. Divisibility Tricks / 68 \\
                 D. More Properties of Congruence / 71 \\
                 E. Linear Congruences and B{\'e}zout's Identity / 72
                 \\
                 6: Congruence Classes / 76 \\
                 A. Congruence Classes (mod $m$): Examples / 76 \\
                 B. Congruence Classes and $\mathbb{Z}/m\mathbb{Z}$ / 80
                 \\
                 C. Arithmetic Modulo $m$ / 82 \\
                 D. Complete Sets of Representatives / 86 \\
                 E. Units / 88 \\
                 7: Applications of Congruences / 91 \\
                 A. Round Robin Tournaments / 91 \\
                 B. Pseudorandom Numbers / 92 \\
                 C. Factoring Large Numbers by Trial Division / 100 \\
                 D. Sieves / 103 \\
                 E. Factoring by the Pollard Rho Method / 105 \\
                 F. Knapsack Cryptosystems / 111 \\
                 8: Rings and Fields / 118 \\
                 A. Axioms / 118 \\
                 B. $\mathbb{Z}/m\mathbb{Z}$ / 124 \\
                 C. Homomorphisms / 127 \\
                 9: Fermat's and Euler's Theorems / 134 \\
                 A. Orders of Elements / 134 \\
                 B. Fermat's Theorem / 138 \\
                 C. Euler's Theorem / 141 \\
                 D. Finding High Powers Modulo $m$ / 145 \\
                 E. Groups of Units and Euler's Theorem / 147 \\
                 F. The Exponent of an Abelian Group / 152 \\
                 10: Applications of Fermat's and Euler's Theorems / 155
                 \\
                 A. Fractions in Base $a$ / 155 \\
                 B. RSA Codes / 164 \\
                 C. 2-Pseudoprimes / 169 \\
                 D. Trial $a$-Pseudoprime Testing / 175 \\
                 E. The Pollard $p - 1$ Algorithm / 177 \\
                 11: On Groups / 180 \\
                 A. Subgroups / 180 \\
                 B. Lagrange's Theorem / 182 \\
                 C. A Probabilistic Primality Test / 185 \\
                 D. Homomorphisms / 186 \\
                 E. Some Nonabelian Groups / 189 \\
                 12: The Chinese Remainder Theorem / 194 \\
                 A. The Theorem / 194 \\
                 B. Products of Rings and Euler's $\phi$-Function / 202
                 \\
                 C. Square Roots of $1$ Modulo $m$ / 205 \\
                 13: Matrices and Codes / 208 \\
                 A. Matrix Multiplication / 209 \\
                 B. Linear Equations / 212 \\
                 C. Determinants and Inverses / 214 \\
                 D. $M_n(R)$ / 215 \\
                 E. Error-Correcting Codes, $I$ / 217 \\
                 F. Hill Codes / 224 \\
                 14: Polynomials / 231 \\
                 15: Unique Factorization / 239 \\
                 A. Division Theorem / 239 \\
                 B. Primitive Roots / 243 \\
                 C. Greatest Common Divisors / 245 \\
                 D. Factorization into Irreducible Polynomials / 249 \\
                 16: The Fundamental Theorem of Algebra / 253 \\
                 A. Rational Functions / 254 \\
                 B. Partial Fractions / 255 \\
                 C. Irreducible Polynomials over $\mathbb{R}$ / 258 \\
                 D. The Complex Numbers / 260 \\
                 E. Root Formulas / 263 \\
                 F. The Fundamental Theorem / 269 \\
                 G. Integrating / 273 \\
                 17: Derivatives / 277 \\
                 A. The Derivative of a Polynomial / 277 \\
                 B. Sturm's Algorithm / 280 \\
                 18: Factoring in $\mathbb{Q}[x], I$ / 286 \\
                 A. Gauss's Lemma / 286 \\
                 B. Finding Roots / 289 \\
                 C. Testing for Irreducibility / 291 \\
                 19: The Binomial Theorem in Characteristic $p$ / 293
                 \\
                 A. The Binomial Theorem / 293 \\
                 B. Fermat's Theorem Revisited / 297 \\
                 C. Multiple Roots / 300 \\
                 20: Congruences and the Chinese Remainder Theorem / 302
                 \\
                 A. Congruences Modulo a Polynomial / 302 \\
                 B. The Chinese Remainder Theorem / 308 \\
                 21: Applications of the Chinese Remainder Theorem / 310
                 \\
                 A. The Method of Lagrange Interpolation / 310 \\
                 B. Fast Polynomial Multiplication / 313 \\
                 22: Factoring in $\mathbb{F}_p[x]$ and in
                 $\mathbb{Z}[x]$ / 323 \\
                 A. Berlekamp's Algorithm / 323 \\
                 B. Factoring in $\mathbb{Z}[x]$ by Factoring mod $M$ /
                 333 \\
                 C. Bounding the Coefficients of Factors of a Polynomial
                 / 334 \\
                 D. Factoring Modulo High Powers of Primes / 338 \\
                 23: Primitive Roots / 346 \\
                 A. Primitive Roots Modulo $m$ / 346 \\
                 B. Polynomials Which Factor Modulo Every Prime / 351
                 \\
                 24: Cyclic Groups and Primitive Roots / 353 \\
                 A. Cyclic Groups / 353 \\
                 B. Primitive Roots Modulo $p^e$ / 356 \\
                 25: Pseudoprimes / 363 \\
                 A. Lots of Carmichael Numbers / 363 \\
                 B. Strong $a$-Pseudoprimes / 368 \\
                 C. Rabin's Theorem / 372 \\
                 26: Roots of Unity in $\mathbb{Z}/m\mathbb{Z}$ / 378
                 \\
                 A. For Which a Is $m$ an $a$-Pseudoprime? / 378 \\
                 B. Square Roots of $- 1$ in $\mathbb{Z}/p\mathbb{Z}$ /
                 381 \\
                 C. Roots of $- 1$ in $\mathbb{Z}/m\mathbb{Z}$ / 382 \\
                 D. False Witnesses / 385 \\
                 E. Proof of Rabin's Theorem / 388 \\
                 F. RSA Codes and Carmichael Numbers / 392 \\
                 27: Quadratic Residues / 397 \\
                 A. Reduction to the Odd Prime Case / 397 \\
                 B. The Legendre Symbol / 399 \\
                 C. Proof of Quadratic Reciprocity / 405 \\
                 D. Applications of Quadratic Reciprocity / 407 \\
                 28: Congruence Classes Modulo a Polynomial / 414 \\
                 A. The Ring $\mathbb{F}[x]/m(x)$ / 414 \\
                 B. Representing Congruence Classes mod $m(x)$ / 418 \\
                 C. Orders of Elements / 422 \\
                 D. Inventing Roots of Polynomials / 426 \\
                 E. Finding Polynomials with Given Roots / 428 \\
                 29: Some Applications of Finite Fields / 432 \\
                 A. Latin Squares / 432 \\
                 B. Error Correcting Codes / 438 \\
                 C. Reed-Solomon Codes / 450 \\
                 30: Classifying Finite Fields / 464 \\
                 A. More Homomorphisms / 464 \\
                 B. On Berlekamp's Algorithm / 468 \\
                 C. Finite Fields Are Simple / 469 \\
                 D. Factoring $x^{p^*} - x$ in $F_p[x]$ / 471 \\
                 E. Counting Irreducible Polynomials / 474 \\
                 F. Finite Fields / 477 \\
                 G. Most Polynomials in $\mathbb{Z}[x]$ Are Irreducible
                 / 479 \\
                 Hints to Selected Exercises / 483 \\
                 References / 509 \\
                 Index / 513",
}

@Book{Childs:2009:CIH,
  author =       "Lindsay N. Childs",
  title =        "A Concrete Introduction to Higher Algebra",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "xiv + 603",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-0-387-74725-5",
  ISBN =         "0-387-74527-0, 0-387-74725-7 (e-book)",
  ISBN-13 =      "978-0-387-74527-5, 978-0-387-74725-5 (e-book)",
  LCCN =         "QA155 .C53 2009",
  bibdate =      "Fri Nov 21 14:16:31 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Undergraduate texts in mathematics",
  abstract =     "This book is an informal and readable introduction to
                 higher algebra at the post-calculus level. The concepts
                 of ring and field are introduced through study of the
                 familiar examples of the integers and polynomials. A
                 strong emphasis on congruence classes leads in a
                 natural way to finite groups and finite fields. The new
                 examples and theory are built in a well-motivated
                 fashion and made relevant by many applications --- to
                 cryptography, error correction, integration, and
                 especially to elementary and computational number
                 theory. The later chapters include expositions of
                 Rabin's probabilistic primality test, quadratic
                 reciprocity, the classification of finite fields, and
                 factoring polynomials over the integers. Over 1000
                 exercises, ranging from routine examples to extensions
                 of theory, are found throughout the book; hints and
                 answers for many of them are included in an
                 appendix.\par

                 The new edition includes topics such as Luhn's formula,
                 Karatsuba multiplication, quotient groups and
                 homomorphisms, Blum--Blum--Shub pseudorandom numbers,
                 root bounds for polynomials, Montgomery multiplication,
                 and more.",
  acknowledgement = ack-nhfb,
  subject =      "Algebra",
  tableofcontents = "Numbers \\
                 Induction \\
                 Euclid's algorithm \\
                 Unique factorization \\
                 Congruence \\
                 Congruence classes and rings \\
                 Congruence classes \\
                 Rings and fields \\
                 Matrices and codes \\
                 Congruences and groups \\
                 Fermat's and Euler's theorems \\
                 Applications of Euler's theorem \\
                 Groups \\
                 The Chinese remainder theorem \\
                 Polynomials \\
                 Unique factorization \\
                 The fundamental theorem of algebra \\
                 Polynomials in $\mathbb{Q}[x]$ \\
                 Congruences and the Chinese remainder theorem \\
                 Fast polynomial multiplication \\
                 Primitive roots \\
                 Cyclic groups and cryptography \\
                 Carmichael numbers \\
                 Quadratic reciprocity \\
                 Quadratic applications \\
                 Finite fields \\
                 Congruence classes modulo a polynomial \\
                 Homomorphisms and finite fields \\
                 BCH codes \\
                 Factoring polynomials \\
                 Factoring in $\mathbb{Z}[x]$ \\
                 Irreducible polynomials",
}

@Book{Conway:1990:CFA,
  author =       "John B. Conway",
  title =        "A Course in Functional Analysis",
  volume =       "96",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xvi + 399",
  year =         "1990",
  ISBN =         "0-387-97245-5 (New York), 3-540-97245-5 (Berlin)",
  ISBN-13 =      "978-0-387-97245-9 (New York), 978-3-540-97245-7
                 (Berlin)",
  LCCN =         "QA320 .C658 1990",
  MRclass =      "46-01 (47-01)",
  MRnumber =     "1070713 (91e:46001)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Graduate Texts in Mathematics",
  URL =          "http://catdir.loc.gov/catdir/enhancements/fy0813/97122669d.html;
                 http://catdir.loc.gov/catdir/enhancements/fy0813/97122669t.html;
                 http://www.gbv.de/dms/bowker/toc/9780387972459.pdf;
                 http://www.gbv.de/dms/ilmenau/toc/025248731.PDF;
                 http://www.loc.gov/catdir/enhancements/fy0813/97122669-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0813/97122669-t.html;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0706.46003",
  ZMnumber =     "0706.46003",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface / vii \\
                 Preface to the Second Edition / xi \\
                 I: Hilbert Spaces \\
                 1. Elementary Properties and Examples / 1 \\
                 2. Orthogonality / 7 \\
                 3. The Riesz Representation Theorem / 11 \\
                 4. Orthonormal Sets of Vectors and Bases / 14 \\
                 5. Isomorphic Hilbert Spaces and the Fourier Transform
                 for the Circle / 19 \\
                 6. The Direct Sum of Hilbert Spaces / 23 \\
                 II: Operators on Hilbert Space \\
                 1. Elementary Properties and Examples / 26 \\
                 2. The Adjoint of an Operator / 31 \\
                 3. Projections and Idempotents; Invariant and Reducing
                 Subspaces / 36 \\
                 4. Compact Operators / 41 \\
                 5.* The Diagonalization of Compact Seif-Adjoint
                 Operators / 46 \\
                 6.* An Application: Sturm--Liouville Systems / 49 \\
                 7.* The Spectral Theorem and Functional Calculus for
                 Compact Normal Operators / 54 \\
                 8.* Unitary Equivalence for Compact Normal Operators /
                 60 \\
                 III: Banach Spaces \\
                 1. Elementary Properties and Examples / 63 \\
                 2. Linear Operators on Normed Spaces / 67 \\
                 3. Finite Dimensional Normed Spaces / 69 \\
                 4. Quotients and Products of Normed Spaces / 70 \\
                 5. Linear Functionals / 73 \\
                 6. The Hahn--Banach Theorem / 77 \\
                 7.* An Application: Banach Limits / 82 \\
                 8.* An Application: Runge's Theorem / 83 \\
                 9.* An Application: Ordered Vector Spaces / 86 \\
                 10. The Dual of a Quotient Space and a Subspace / 88
                 \\
                 11. Reflexive Spaces / 89 \\
                 12. The Open Mapping and Closed Graph Theorems / 90 \\
                 13. Complemented Subspaces of a Banach Space / 93 \\
                 14. The Principle of Uniform Boundedness / 95 \\
                 IV: Locally Convex Spaces \\
                 1. Elementary Properties and Examples / 99 \\
                 2. Metrizable and Normable Locally Convex Spaces / 105
                 \\
                 3. Some Geometric Consequences of the Hahn--Banach
                 Theorem / 108 \\
                 4.* Some Examples of the Dual Space of a Locally Convex
                 Space / 114 \\
                 5.* Inductive Limits and the Space of Distributions /
                 116 \\
                 V: Weak Topologies \\
                 1 Duality / 124 \\
                 2. The Dual of a Subspace and a Quotient Space / 128
                 \\
                 3. Alao{\u{g}}lu's Theorem / 130 \\
                 4. Reflexivity Revisited / 131 \\
                 5. Separability and Metrizability / 134 \\
                 6. An Application: The Stone--Cech Compactification /
                 137 \\
                 7. The Krein--Milman Theorem / 141 \\
                 8. An Application: The Stone--Weierstrass Theorem / 145
                 \\
                 9 The Schauder Fixed Point Theorem / 149 \\
                 10. The Ryll--Nardzewski Fixed Point Theorem / 151 \\
                 11 An Application: Haar Measure on a Compact Group /
                 154 \\
                 12. The Krein--Smulian Theorem / 159 \\
                 13. Weak Compactness / 163 \\
                 VI: Linear Operators on a Banach Space \\
                 1. The Adjoint of a Linear Operator / 166 \\
                 2.* The Banach--Stone Theorem / 171 \\
                 3. Compact Operators / 173 \\
                 4. Invariant Subspaces / 178 \\
                 5. Weakly Compact Operators / 183 \\
                 VII: Banach Algebras and Spectral Theory for Operators
                 on a Banach Space \\
                 1 Elementary Properties and Examples / 187 \\
                 2 Ideals and Quotients / 191 \\
                 3. The Spectrum / 195 \\
                 4. The Riesz Functional Calculus / 199 \\
                 5, Dependence of the Spectrum on the Algebra / 205 \\
                 6. The Spectrum of a Linear Operator / 208 \\
                 7. The Spectral Theory of a Compact Operator / 214 \\
                 8 Abelian Banach Algebras / 218 \\
                 9 The Group Algebra of a Locally Compact Abelian Group
                 / 223 \\
                 VIII: $C^*$-Algebras \\
                 1. Elementary Properties and Examples / 232 \\
                 2. Abelian $C^*$-Algebras and the Functional Calculus
                 in $C^*$-Algebras / 236 \\
                 3. The Positive Elements in a $C^*$-Algebra / 240 \\
                 4.* Ideals and Quotients of $C^*$-Algebras / 245 \\
                 5.* Representations of $C^*$-Algebras and the
                 Gelfand--Naimark--Segal Construction / 248 \\
                 IX: Normal Operators on Hubert Space \\
                 1. Spectral Measures and Representations of Abelian
                 $C^*$-Algebras / 255 \\
                 2. The Spectral Theorem / 262 \\
                 3. Star-Cyclic Normal Operators / 268 \\
                 4. Some Applications of the Spectral Theorem / 271 \\
                 5. Topologies on $\mathcal{B}(\mathcal{H})$ / 274 \\
                 6. Commuting Operators / 276 \\
                 7. Abelian von Neumann Algebras / 281 \\
                 8. The Functional Calculus for Normal Operators: The
                 Conclusion of the Saga / 285 \\
                 9. Invariant Subspaces for Normal Operators / 290 \\
                 10. Multiplicity Theory for Normal Operators: A
                 Complete Set of Unitary Invariants / 293 \\
                 X: Unbounded Operators \\
                 1. Basic Properties and Examples / 303 \\
                 2. Symmetric and Self-Adjoint Operators / 308 \\
                 3. The Cayley Transform / 316 \\
                 4. Unbounded Normal Operators and the Spectral Theorem
                 / 319 \\
                 5. Stone's Theorem / 327 \\
                 6. The Fourier Transform and Differentiation / 334 \\
                 7. Moments / 343 \\
                 XI: Fredholm Theory \\
                 1. The Spectrum Revisited / 347 \\
                 2. Fredholm Operators / 349 \\
                 3. The Fredholm Index / 352 \\
                 4. The Essential Spectrum / 358 \\
                 5. The Components of ${\cal S F}$ / 362 \\
                 6. A Finer Analysis of the Spectrum / 363 \\
                 Appendix A: Preliminaries \\
                 1. Linear Algebra / 369 \\
                 2. Topology / 371 \\
                 Appendix B \\
                 The Dual of $L^p(\mu)$ / 375 \\
                 Appendix C \\
                 The Dual of $C_o(X)$ / 378 \\
                 Bibliography / 384 \\
                 List of Symbols / 391 \\
                 Index / 395",
}

@Book{Courant:1924:MMP,
  author =       "Richard Courant and David Hilbert",
  title =        "{Methoden der mathematischen Physik}. ({German})
                 [{Methods} of Mathematical Physics]",
  volume =       "1",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiii + 450",
  year =         "1924",
  LCCN =         "",
  bibdate =      "Sun Nov 23 16:29:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Die Grundlehren der mathematischen Wissenschaften
                 (12)",
  acknowledgement = ack-nhfb,
  author-dates = "Richard Courant (1888--1972); David Hilbert
                 (1862--1943)",
  language =     "German",
}

@Book{Courant:1937:MMP,
  author =       "Richard Courant and David Hilbert",
  title =        "{Methoden der mathematischen Physik}. ({German})
                 [{Methods} of Mathematical Physics]",
  volume =       "2",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 549",
  year =         "1937",
  LCCN =         "",
  bibdate =      "Sun Nov 23 16:29:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Die Grundlehren der mathematischen Wissenschaften
                 (48)",
  acknowledgement = ack-nhfb,
  author-dates = "Richard Courant (1888--1972)",
  language =     "German",
}

@Book{Courant:1942:MMP,
  author =       "Richard Courant and David Hilbert",
  title =        "{Methoden der mathematischen Physik}. ({German})
                 [{Methods} of Mathematical Physics]",
  volume =       "2",
  publisher =    "Interscience",
  address =      "New York, NY, USA",
  pages =        "xiv + 549",
  year =         "1942",
  LCCN =         "????",
  bibdate =      "Sun Nov 23 16:29:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Die Grundlehren der mathematischen Wissenschaften
                 (48)",
  acknowledgement = ack-nhfb,
  author-dates = "Richard Courant (1888--1972)",
  language =     "German",
}

@Book{Courant:1953:MMP,
  author =       "Richard Courant and David Hilbert",
  title =        "Methods of Mathematical Physics",
  volume =       "I",
  publisher =    "Interscience Publishers, Inc.",
  address =      "New York, NY, USA",
  pages =        "xv + 561",
  year =         "1953",
  ISBN =         "0-471-50447-5, 0-585-29428-3 (e-book)",
  ISBN-13 =      "978-0-471-50447-4, 978-0-585-29428-5 (e-book)",
  LCCN =         "????",
  MRclass =      "79.0X",
  MRnumber =     "0065391 (16,426a)",
  MRreviewer =   "J. B. Diaz",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "Richard Courant (1888--1972); David Hilbert
                 (1862--1943)",
  remark =       "Republication of Julius Springer, Berlin, 1937
                 edition.",
}

@Book{Courant:1968:MMPa,
  author =       "Richard Courant and David Hilbert",
  title =        "{Methoden der mathematischen Physik}. ({German})
                 [{Methods} of Mathematical Physics]",
  volume =       "1",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "xv + 469",
  year =         "1968",
  ISBN =         "0-387-04177-X (New York), 3-540-04177-X (Berlin)",
  ISBN-13 =      "978-0-387-04177-3 (New York), 978-3-540-04177-1
                 (Berlin)",
  LCCN =         "????",
  bibdate =      "Sun Nov 23 16:42:09 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Heidelberger Taschenb{\"u}cher (30)",
  acknowledgement = ack-nhfb,
  author-dates = "Richard Courant (1888--1972); David Hilbert
                 (1862--1943)",
  language =     "German",
  tableofcontents = "Erstes Kapitel \\
                 Die Algebra der linearen Transformationen und
                 quadratischen Formen \\
                 \S 1. Lineare Gleichungen und lineare Transformationen
                 / 1 \\
                 1. Vektoren / 1 \\
                 2. Orthogonale Vektorensysteme. Vollst{\"a}ndigkeit / 3
                 \\
                 3. Lineare Transformationen, Matrizen / 5 \\
                 4. Bilinearformen, quadratische und hermitesche Formen
                 / 10 \\
                 5. Orthogonale und unit{\"a}re Transformationen / 13
                 \\
                 \S 2. Lineare Transformationen mit linearem Parameter /
                 14 \\
                 \S 3. Die Hauptachsentransformation der quadratischen
                 und Hermiteschen Formen / 19 \\
                 1. Die Durchf{\"u}hrung der Hauptachsentransformation
                 auf Grund eines Maximumprinzips / 20 \\
                 2. Charakteristische Zahlen und Eigenwerte / 22 \\
                 3. Verallgemeinerung auf Hermitesche Formen / 23 \\
                 4. Tr{\"a}gheitsgesetz der quadratischen Formen / 24
                 \\
                 5. Darstellung der Resolvente einer Form / 24 \\
                 6. L{\"o}sung des zu einer Form geh{\"o}rigen linearen
                 Gleichungssystems / 25 \\
                 \S 4. Die Minimum-Maximum-Eigenschaft der Eigenwerte /
                 26 \\
                 1. Kennzeichnung der charakteristischen Zahlen durch
                 ein Minimum-Maximumproblem / 26 \\
                 2. Anwendungen / 28 \\
                 \S 5. Erg{\"a}nzungen und Aufgaben zum ersten Kapitel /
                 29 \\
                 1. Lineare Unabh{\"a}ngigkeit und Gramsche Determinante
                 / 29 \\
                 2. Determinantenabsch{\"a}tzung von Hadamard / 31 \\
                 3. Simultane Transformation zweier quadratischer Formen
                 in kanonische Gestalt / 32 \\
                 4. Bilinearformen und quadratische Formen von unendlich
                 vielen Variablen / 33 \\
                 5. Unendlich kleine lineare Transformationen / 33 \\
                 6. Variierte Systeme / 34 \\
                 7. Die Auferlegung einer Bindung / 36 \\
                 8. Elementarteiler einer Matrix oder einer Bilinearform
                 / 36 \\
                 9. Spektrum einer unit{\"a}ren Matrix / 37 \\
                 Literatur zum ersten Kapitel / 38 \\
                 Zweites Kapitel \\
                 Das Problem der Reihenentwicklung willk{\"u}rlicher
                 Funktionen \\
                 \S 1. Orthogonale Funktionensysteme / 40 \\
                 1. Definitionen / 40 \\
                 2. Orthogonalisierung von Funktionen / 41 \\
                 3. Besselsche Ungleichung.
                 Vollst{\"a}ndigkeitsrelation. Approximation im Mittel /
                 42 \\
                 4. Orthogonale und unit{\"a}re Transformationen in
                 unendhch vielen Ver{\"a}nderlichen / 45 \\
                 5. G{\"u}ltigkeit der Ergebnisse bei mehreren
                 unabh{\"a}ngigen Ver{\"a}nderlichen. Erweiterung der
                 Voraussetzungen / 46 \\
                 6. Erzeugung vollst{\"a}ndiger Funktionensysteme in
                 mehreren Variabeln / 46 \\
                 \S 2. Das H{\"a}ufungsprinzip f{\"u}r Funktionen / 47
                 \\
                 1. Konvergenz im Funktionenraum / 47 \\
                 \S 3. Unabh{\"a}ngigkeitsma{\ss} und Dimensionenzahl /
                 51 \\
                 1. Unabh{\"a}ngigkeitsma{\ss} / 51 \\
                 2. Asymptotische Dimensionenzahl einer Funktionenfolge
                 / 53 \\
                 \S 4. Der Weierstra{\ss}sche Approximationssatz.
                 Vollst{\"a}ndigkeit der Potenzen und der
                 trigonometrischen Funktionen / 55 \\
                 1. Der Weierstra{\ss}sche Approximationssatz / 55 \\
                 2. Ausdehnung des Ergebnisses auf Funktionen von
                 mehreren Ver{\"a}nderlichen / 57 \\
                 3. Gleichzeitige Approximation der Ableitungen / 57 \\
                 4. Vollst{\"a}ndigkeit der trigonometrischen Funktionen
                 / 57 \\
                 \S 5. Die Fouriersche Reihe / 58 \\
                 1. Beweis des Hauptsatzes / 58 \\
                 2. Mehrfache Fouriersche Reihen / 62 \\
                 3. Die Gr{\"o}{\ss}enordnung der Fourierschen
                 Entwicklungskoeffizienten / 62 \\
                 4. Streckung des Grundgebietes / 63 \\
                 5. Einige Beispiele / 63 \\
                 \S 6. Das Fouriersche Integral / 65 \\
                 1. Beweis des Hauptsatzes / 65 \\
                 2. Ausdehnung des Resultates auf mehr Variable / 67 \\
                 3. Reziprozit{\"a}tsformeln / 68 \\
                 \S 7. Beispiele f{\"u}r das Fouriersche Integral / 69
                 \\
                 \S 8. Die Polynome von Legendre / 70 \\
                 1. Erzeugung durch Orthogonalisierung der Potenzen $1,
                 x, x^2$ / 70 \\
                 2. Die erzeugende Funktion / 72 \\
                 3. Weitere Eigenschaften / 73 \\
                 \S 9. Beispiele anderer Orthogonalsysteme / 74 \\
                 1. Verallgemeinerung der zu den Legendreschen Polynomen
                 f{\"u}hrenden Fragestellung / 74 \\
                 2. Die Tschebyscheffschen Polynome / 75 \\
                 3. Die Jacobischen Polynome / 76 \\
                 4. Die Hermiteschen Polynome / 77 \\
                 5. Die Laguerreschen Polynome / 79 \\
                 6. Vollst{\"a}ndigkeit der Laguerreschen und
                 Hermiteschen Polynome / 81 \\
                 \S 10. Erg{\"a}nzungen und Aufgaben zum zweiten Kapitel
                 / 82 \\
                 1. Die Hurwitzsche L{\"o}sung des isoperimetrischen
                 Problems / 82 \\
                 2. Reziprozit{\"a}tsformeln / 83 \\
                 3. Fouriersches Integral und mittlere Konvergenz / 84
                 \\
                 4. Spektrale Zerlegung durch Fouriersche Reihe und
                 Fouriersches Integral / 85 \\
                 5. Dichte Funktionensysteme / 85 \\
                 6. Ein Satz von H. M{\"u}ntz {\"u}ber die
                 Vollst{\"a}ndigkeit von Potenzen / 86 \\
                 7. Der Fejersche Summationssatz / 86 \\
                 8. Die Mellinschen Umkehrformeln / 87 \\
                 9. Das Gibbssche Ph{\"a}nomen / 90 \\
                 10. Ein Satz {\"u}ber die Gramsche Determinante / 91
                 \\
                 11. Anwendung des Lebesgueschen Integralbegriffes / 92
                 \\
                 Literatur zum zweiten Kapitel / 94 \\
                 Drittes Kapitel \\
                 Theorie der linearen Integralgleichungen \\
                 \S 1. Vorbereitende Betrachtungen / 96 \\
                 1. Bezeichnungen und Grundbegriffe / 96 \\
                 2. Quellenm{\"a}{\ss}ig dargestellte Funktionen / 97
                 \\
                 3. Ausgeartete Kerne / 98 \\
                 \S 2. Die Fredholmschen S{\"a}tze f{\"u}r ausgeartete
                 Kerne / 99 \\
                 \S 3. Die Fredholmschen S{\"a}tze f{\"u}r einen
                 beliebigen Kern / 101 \\
                 \S 4. Die symmetrischen Kerne und ihre Eigenwerte / 104
                 \\
                 1. Existenz eines Eigenwertes bei einem symmetrischen
                 Kern / 104 \\
                 2. Die Gesamtheit der Eigenfunktionen und Eigenwerte /
                 1073 \\
                 Die Maximum-Minimum-Eigenschaft der Eigenwerte / 112
                 \\
                 \S 5. Der Entwicklungssatz und seine Anwendungen / 114
                 \\
                 1. Der Entwicklungssatz / 114 \\
                 2. Aufl{\"o}sung der inhomogenen linearen
                 Integralgleichung / 115 \\
                 3. Die Bilinearformel f{\"u}r die iterierten Kerne /
                 116 \\
                 4. Der Mercersche Satz / 117 \\
                 \S 6. Die Neumannsche Reihe und der reziproke Kern /
                 119 \\
                 \S 7. Die Fredholmschen Formeln / 121 \\
                 \S 8. Neubegr{\"u}ndung der Theorie / 124 \\
                 1. Ein Hilfssatz / 125 \\
                 2. Die Eigenfunktionen eines symmetrischen Kernes / 126
                 \\
                 3. Unsymmetrische Kerne / 127 \\
                 4. Stetige Abh{\"a}ngigkeit der Eigenwerte und
                 Eigenfunktionen vom Kern / 128 \\
                 \S 9. Erweiterung der G{\"u}ltigkeitsgrenzen der
                 Theorie / 128 \\
                 \S 10. Erg{\"a}nzungen und Aufgaben zum dritten Kapitel
                 / 130 \\
                 1. Beispiele / 130 \\
                 2. Singulare Integralgleichungen / 130 \\
                 3. Methode von E. Schmidt zur Herleitung der S{\"a}tze
                 von Fredholm / 131 \\
                 4. Methode von Enskog zur Aufl{\"o}sung symmetrischer
                 Integralgleichungen / 132 \\
                 5. Methode von Kellogg zur Bestimmung von
                 Eigenfunktionen / 132 \\
                 6. Symbolische Funktionen eines Kerns und ihre
                 Eigenwerte / 132 \\
                 J. Beispiel eines unsymmetrischen Kerns ohne
                 Null{\"o}sungen / 133 \\
                 8. Volterrasche Integralgleichungen / 133 \\
                 9. Abelsche Integralgleichung / 134 \\
                 10. Die zu einem unsymmetrischen Kerne geh{\"o}rigen
                 adjungierten Orthogonalsysteme / 134 \\
                 11. Integralgleichungen erster Art / 135 \\
                 12. Die Methode der unendlich vielen Variablen / 136
                 \\
                 13. Minimumeigenschaften der Eigenfunktionen / 136 \\
                 14. Polare Integralgleichungen / 136 \\
                 15. Symmetrisierbare Kerne / 137 \\
                 16. Bestimmung des l{\"o}senden Kernes durch
                 Funktionalgleichungen / 137 \\
                 17. Die Stetigkeit der definiten Kerne / 137 \\
                 18. Satz von Hammerstein / 137 \\
                 Literatur zum dritten Kapitel / 137 \\
                 Viertes Kapitel \\
                 Die Grundtatsachen der Variationsrechnung \\
                 \S 1. Die Problemstellung der Variationsrechnung / 139
                 \\
                 1. Maxima und Minima von Funktionen / 139 \\
                 2. Funktionenfunktionen / 142 \\
                 3. Die typischen Probleme der Variationsrechnung / 144
                 \\
                 4. Die charakteristischen Schwierigkeiten der
                 Variationsrechnung / 147 \\
                 \S 2. Ans{\"a}tze zur direkten L{\"o}sung / 148 \\
                 1. Isoperimetrisches Problem / 149 \\
                 2. Das Ritzsche Verfahren. Minimalfolgen / 149 \\
                 3. Weitere direkte Methoden. Differenzenverfahren.
                 Unendlich viele Ver{\"a}nderliche / 151 \\
                 4. Prinzipielles {\"u}ber die direkten Methoden der
                 Variationsrechnung / 156 \\
                 \S 3. Die Eulerschen Gleichungen der Variationsrechnung
                 / 157 \\
                 1. Das einfachste Problem der Variationsrechnung / 158
                 \\
                 2. Mehrere gesuchte Funktionen / 161 \\
                 3. Auftreten h{\"o}herer Ableitungen / 163 \\
                 4. Mehrere unabh{\"a}ngige Variable / 164 \\
                 5. Identisches Verschwinden des Eulerschen
                 Differentialausdruckes. Divergenzausdr{\"u}cke / 165
                 \\
                 6. Homogene Form der Eulerschen Differentialgleichungen
                 / 168 \\
                 7. Variationsprobleme mit Erweiterung der
                 Zulassungsbedingungen. S{\"a}tze von du Bois-Reymond
                 und Haar / 171 \\
                 8. Andere Variationsprobleme und ihre
                 Funktionalgleichungen / 176 \\
                 \S 4. Bemerkungen und Beispiele zur Integration der
                 Eulerschen Differentialgleichung / 177 \\
                 \S 5. Randbedingungen / 179 \\
                 1. Nat{\"u}rliche Randbedingungen bei freien
                 R{\"a}ndern / 179 \\
                 2. Geometrische Probleme. Transversalit{\"a}t / 181 \\
                 \S 6. Die zweite Variation und die Legendresche
                 Bedingung / 184 \\
                 \S 7. Variationsprobleme mit Nebenbedingungen / 186 \\
                 1. Isoperimetrische Probleme / 187 \\
                 2. Endliche Bedingungsgleichungen / 189 \\
                 3. Differentialgleichungen als Nebenbedingungen / 191
                 \\
                 \S 8. Der invariante Charakter der Eulerschen
                 Differentialgleichungen / 192 \\
                 1. DerEulersche Ausdruck als Gradient im
                 Funktionenraume. Invarianz des Eulerschen Ausdruckes /
                 192 \\
                 2. Transformationen von A u. Polarkoordinaten / 194 \\
                 3. Elliptische Koordinaten / 195 \\
                 \S 9. Transformation von Variationsproblemen in die
                 kanonische und involutorische Gestalt / 199 \\
                 1. Transformation bei gew{\"o}hnlichen Minimumproblemen
                 mit Nebenbedingungen / 199 \\
                 2. Die involutorische Transformation der einfachsten
                 Variationsprobleme / 201 \\
                 3. Die Transformation des Variationsproblems in die
                 kanonische Gestalt / 206 \\
                 4. Verallgemeinerungen / 207 \\
                 \S 10. Variationsrechnung und Differentialgleichungen
                 der mathematischen Physik / 210 \\
                 1. Allgemeines / 210 \\
                 2. Schwingende Saite (Seil) und schwingender Stab / 212
                 \\
                 3. Membran und Platte / 214 \\
                 \S 11. Erg{\"a}nzungen und Aufgaben zum vierten Kapitel
                 / 219 \\
                 1. Variationsproblem zu gegebener Differentialgleichung
                 / 219 \\
                 2. Reziprozit{\"a}t bei isoperimetrischen Problemen /
                 219 \\
                 3. Kreisf{\"o}rmige Lichtstrahlen / 219 \\
                 4. Das Problem der Dido / 219 \\
                 5. Beispiel eines r{\"a}umlichen Problems / 219 \\
                 6. Das isoperimetrische Problem auf einer krummen
                 Fl{\"a}che / 220 \\
                 7. Die Indikatrix und ihre Anwendungen / 220 \\
                 8. Variation bei ver{\"a}nderlichem Gebiet / 221 \\
                 9. Die S{\"a}tze von E. Noether {\"u}ber invariante
                 Variationsprobleme. Integrale in der Punktmechanik /
                 223 \\
                 10. Transversalit{\"a}t bei mehrfachen Integralen / 226
                 \\
                 11. Eulersche Differentialausdr{\"u}cke auf krummen
                 Fl{\"a}chen / 227 \\
                 12. Das Thomsonsche Prinzip der Elektrostatik / 227 \\
                 13. Gleichgewichtsprobleme beim elastischen K{\"o}rper.
                 Prinzip von Castigliano / 228 \\
                 14. Das Prinzip von Castigliano in der Balkentheorie /
                 230 \\
                 15. Das Variationsproblem der Knickung / 232 \\
                 Literatur zum vierten Kapitel / 233 \\
                 F{\"u}nftes Kapitel Die Schwingungs- und
                 Eigenwertprobleme der mathematischen Physik \\
                 \S 1. Vorbemerkungen {\"u}ber lineare
                 Differentialgleichungen / 234 \\
                 1. Allgemeines. Das Superpositionsprinzip / 234 \\
                 2. Homogene und unhomogene Probleme. Randbedingungen /
                 236 \\
                 3. Formale Beziehungen. Adjungierte
                 Differentialausdr{\"u}cke. Greensche Formeln / 236 \\
                 4. Lineare Funktionalgleichungen als Grenzf{\"a}lle und
                 Analoga von Systemen linearer Gleichungen / 239 \\
                 \S 2. Systeme von endlich vielen Freiheitsgraden / 240
                 \\
                 1. Hauptschwingungen. Normalkoordinaten. Allgemeine
                 Theorie des Bewegungsvorganges / 240 \\
                 2. Allgemeine Eigenschaften der schwingenden Systeme /
                 244 \\
                 \S 3. Die schwingende Saite / 245 \\
                 1. Freie Bewegungen der homogenen Saite / 245 \\
                 2. Erzwungene Bewegungen / 248 \\
                 3. Die allgemeine unhomogene Saite und das
                 Sturm-Liouvillesche Eigenwertproblem / 249 \S 4. Der
                 schwingende Stab / 253 \\
                 \S 5. Die schwingende Membran / 255 \\
                 1. Das allgemeine Eigenwertproblem der homogenen
                 Membran / 255 \\
                 2: Erzwungene Bewegungen / 257 \\
                 3. Knotenlinien / 257 \\
                 4. Rechteckige Membran / 258 \\
                 5. Kreisf{\"o}rmige Membran. Besselsche Funktionen /
                 260 \\
                 6. Die unhomogene Membran / 263 \\
                 \S 6. Die schwingende Platte / 263 \\
                 1. Allgemeines / 263 \\
                 2. Kreisf{\"o}rmige Begrenzung / 264 \\
                 \S 7. Allgemeines {\"u}ber die Methode der
                 Eigenfunktionen / 265 \\
                 1. Die Methode bei Schwingungs- und
                 Gleichgewichtsproblemen / 265 \\
                 2. W{\"a}rmeleitung und Eigenwertprobleme / 268 \\
                 3. Sonstiges Auftreten von Eigenwertproblemen / 269 \\
                 \S 8. Schwingungen dreidimensionaler Kontinua / 269 \\
                 \S 9. Randwertproblem der Potentialtheorie und
                 Eigenfunktionen / 271 \\
                 1. Kreis, Kugel, Kugelschale / 271 \\
                 2. Zylindrisches Gebiet / 274 \\
                 3. Das Lamesche Problem 275 \\
                 \S 10. Probleme vom Sturm-Liouvilleschen Typus.
                 Singulare Randpunkte / 280 \\
                 1. Besselsche Funktionen / 280 \\
                 2. Legendresche Funktionen beliebiger Ordnung / 280 \\
                 3. Jacobische und Tschebyscheffsche Polynome / 282 \\
                 4. Hermitesche und Laguerresche Polynome / 283 \\
                 \S 11. {\"U}ber das asymptotische Verhalten der
                 L{\"o}sungen Sturm-Liouvillescher
                 Differentialgleichungen / 285 \\
                 1. Beschr{\"a}nktheit bei unendlich anwachsender
                 unabh{\"a}ngiger Variabler / 285 \\
                 2. Versch{\"a}rfung des Resultates (Besselsche
                 Funktionen) / 286 \\
                 3. Beschr{\"a}nktheit bei wachsendem Parameter / 288
                 \\
                 4. Asymptotische Darstellung der L{\"o}sungen / 289 \\
                 5. Asymptotische Darstellung der Sturm-Liouvilleschen
                 Eigenfunktionen / 290 \\
                 \S 12. Eigenwertprobleme mit kontinuierlichem Spektrum
                 / 293 \\
                 1. Die trigonometrischen Funktionen / 293 \\
                 2. Die Besselschen Funktionen / 293 \\
                 3. Das Eigenwertproblem der Schwingungsgleichung
                 f{\"u}r die unendliche Ebene / 294 \\
                 4. Das Schr{\"o}dingersche Eigenwertproblem / 294 \\
                 \S 13. St{\"o}rungsrechnung / 296 \\
                 1. Einfache Eigenwerte / 297 \\
                 2. Mehrfache Eigenwerte / 298 \\
                 3. Ein Beispiel zur St{\"o}rungstheorie / 300 \\
                 \S 14. Die Greensche Funktion (Einflu{\ss}funktion) und
                 die Zur{\"u}ckf{\"u}hrung von
                 Differentialgleichungsproblemen auf Integralgleichungen
                 / 302 \\
                 1. Die Greensche Funktion und das Randwertproblem
                 f{\"u}r gew{\"o}hnliche Differentialgleichungen / 302
                 \\
                 2. Die Konstruktion der Greenschen Funktion und die
                 Greensche Funktion im erweiterten Sinne / 306 \\
                 3. {\"A}quivalenz von Differentialgleichungs- und
                 Integralgleichungsproblem / 309 \\
                 4. Gew{\"o}hnliche Differentialgleichungen h{\"o}herer
                 Ordnung / 313 \\
                 5. Partielle Differentialgleichungen / 314 \\
                 \S 15. Beispiele f{\"u}r Greensche Funktionen / 321 \\
                 1. Gew{\"o}hnliche Differentialgleichungen / 321 \\
                 2. Greensche Funktion von $\Delta u$ f{\"u}r Kreis und
                 Kugel / 326 \\
                 3. Greensche Funktion und konforme Abbildung / 327 \\
                 4. Die Greensche Funktion der Potentialgleichung
                 f{\"u}r eine Kugeloberfl{\"a}che / 327 \\
                 5. Die Greensche Funktion der Gleichung $\Delta u = 0$
                 f{\"u}r ein Rechtflach / 328 \\
                 6. Die Greensche Funktion von $\Delta u$ f{\"u}r das
                 Innere eines Rechtecks / 3337 \\
                 Die Greensche Funktion f{\"u}r einen Kreisring / 335
                 \\
                 \S 16. Erg{\"a}nzungen zum f{\"u}nften Kapitel / 337
                 \\
                 1. Beispiele zur schwingenden Saite / 337 \\
                 2. Schwingungen des frei herabh{\"a}ngenden Seils und
                 Besselsche Funktionen / 338 \\
                 3. Weitere Beispiele f{\"u}r explizit l{\"o}sbare
                 F{\"a}lle der Schwingungsgleichung. Funktionen von
                 Mathieu / 339 \\
                 4. Parameter in den Randbedingungen / 340 \\
                 5. Greensche Tensoren f{\"u}r
                 Differentialgleichungssysteme / 341 \\
                 6. Analytische Fortsetzung der L{\"o}sungen der
                 Gleichung $\Delta u + \lambda u = 0$ / 342 \\
                 7. Ein Satz {\"u}ber die Knotenlinien der L{\"o}sungen
                 von $\Delta u + \lambda u = 0$ / 342 \\
                 8. Beispiel f{\"u}r einen Eigenwert unendlich hoher
                 Ordnung / 342 \\
                 9. Grenzen f{\"u}r die G{\"u}ltigkeit der
                 Entwicklungss{\"a}tze. / 343 \\
                 Literatur zum f{\"u}nften Kapitel / 343 \\
                 Sechstes Kapitel \\
                 Anwendung der Variationsrechnung auf die
                 Eigenwertprobleme \\
                 \S 1. Die Extremumseigenschaften der Eigenwerte / 345
                 \\
                 1. Die klassischen Extremumseigenschaften / 345 \\
                 2. Erg{\"a}nzungen und Verallgemeinerungen / 348 \\
                 3. Eigenwertprobleme f{\"u}r Bereiche mit getrennten
                 Bestandteilen / 351 \\
                 4. Die Maximum-MinimumEigenschaft der Eigenwerte / 351
                 \\
                 \S 2. Allgemeine Folgerungen aus den
                 Extremumseigenschaften der Eigenwerte / 353 \\
                 1. Allgemeine S{\"a}tze / 353 \\
                 2. Das unendliche Anwachsen der Eigenwerte / 358 \\
                 3. Asymptotisches Verhalten der Eigenwerte beim
                 Sturm--Liouvilleschen Problem / 360 \\
                 4. Singulare Differentialgleichungen / 361 \\
                 5. Weitere Bemerkungen {\"u}ber das Anwachsen der
                 Eigenwerte. Auftreten negativer Eigenwerte / 362 \\
                 6. Stetigkeitseigenschaften der Eigenwerte / 363 \\
                 \S 3. Der Vollst{\"a}ndigkeitssatz und der
                 Entwicklungssatz / 368 \\
                 1. Die Vollst{\"a}ndigkeit der Eigenfunktionen / 368
                 \\
                 2. Der Entwicklungssatz / 370 \\
                 3. Versch{\"a}rfung des Entwicklungssatzes / 371 \\
                 \S 4. Die asymptotische Verteilung der Eigenwerte / 373
                 \\
                 1. Die Differentialgleichung $\Delta u + \lambda u = 0$
                 f{\"u}r ein Rechteck / 373 \\
                 2. Die Differentialgleichung $\Delta u + \lambda u = 0$
                 bei Gebieten, welche aus endlich vielen Quadraten oder
                 W{\"u}rfeln bestehen / 374 \\
                 3. Ausdehnung des Resultates auf die allgemeine
                 Differentialgleichung $L[u] + \lambda \rho u = / 0$ \\
                 / 377 \\
                 4. Die Gesetze der asymptotischen Eigenwertverteilung
                 f{\"u}r einen beliebigen Bereich / 379 \\
                 5. Die Gesetze der asymptotischen Eigenwertverteilung
                 f{\"u}r die Differentialgleichung $\Delta u + \lambda u
                 = 0$ in versch{\"a}rfter Form / 385 \\
                 \S 5. Eigenwertprobleme vom Schr{\"o}dingerschen Typus
                 / 387 \\
                 \S 6. Die Knoten der Eigenfunktionen / 392 \\
                 \S 7. Erg{\"a}nzungen und Aufgaben zum sechsten Kapitel
                 / 397 \\
                 1. Ableitung der Minimumeigenschaften der Eigenwerte
                 aus ihrer Vollst{\"a}ndigkeit / 397 \\
                 2. Charakterisierung der ersten Eigenfunktion durch
                 ihre Nullstellenfreiheit / 398 \\
                 3. Andere Minimumeigenschaften der Eigenwerte / 399 \\
                 4. Asymptotische Eigenwertverteilung bei der
                 schwingenden Platte / 400 \\
                 5. bis 7. Aufgaben / 400 \\
                 8. Parameter in den Randbedingungen / 400 \\
                 9. Eigenwertprobleme f{\"u}r geschlossene Fl{\"a}chen /
                 401 \\
                 10. Eigenwertabsch{\"a}tzungen beim Auftreten von
                 singul{\"a}ren Punkten / 401 \\
                 11. Minimums{\"a}tze f{\"u}r Membran und Platte / 402
                 \\
                 12. Minimumprobleme bei variabler Massenverteilung /
                 403 \\
                 13. Knotenpunkte beim Sturm-Liouvilleschen Problem und
                 Maximum-Minimum-Prinzip / 403 \\
                 Literatur zum sechsten Kapitel / 404 \\
                 Siebentes Kapitel \\
                 Spezielle durch Eigenwertprobleme definierte Funktionen
                 \\
                 \S 1. Vorbemerkungen {\"u}ber lineare
                 Differentialgleichungen zweiter Ordnung / 405 \\
                 \S 2. Die Besselschen Funktionen / 406 \\
                 1. Durchf{\"u}hrung der Integraltransformation / 407
                 \\
                 2. Die Hankeischen Funktionen / 407 \\
                 3. Die Besselschen und Neumannschen Funktionen / 410
                 \\
                 4. Integraldarstellungen der Besselschen Funktionen /
                 412 \\
                 5. Eine andere Integraldarstellung der Hankeischen und
                 Besselschen Funktionen / 414 \\
                 6. Potenzreihenentwicklung der Besselschen Funktionen /
                 418 \\
                 7. Relationen zwischen den Besselschen Funktionen / 420
                 \\
                 8. Die Nullstellen der Besselschen Funktionen / 426 \\
                 9. Die Neumannschen Funktionen / 429 \\
                 \S 3. Die Kugelfunktionen von Legendre / 433 \\
                 1. Das Schl{\"a}flische Integral / 433 \\
                 2. Die Integraldarstellungen von Laplace / 435 \\
                 3. Die Legendreschen Funktionen zweiter Art / 435 \\
                 4. Zugeordnete Kugelfunktionen (Legendresche Funktionen
                 h{\"o}herer Ordnung) / 437 \\
                 \S 4. Anwendung der Methode der Integraltransformation
                 auf die Legendreschen, Tschebyscheffschen, Hermiteschen
                 und Laguerreschen Differentialgleichungen / 437 \\
                 1. Legendresche Funktionen / 437 \\
                 2. Die Tschebyscheffschen Funktionen / 439 \\
                 3. Die Hermiteschen Funktionen / 440 \\
                 4. Die Laguerreschen Funktionen / 440 \\
                 \S 5. Die Kugelfunktionen von Laplace / 441 \\
                 1. Aufstellung von $2 n + 1$ Kugelfunktionen $n$ter
                 Ordnung / 442 \\
                 2. Vollst{\"a}ndigkeit des gewonnenen Funktionensystems
                 / 443 \\
                 3. Der Entwicklungssatz / 443 \\
                 4. Das Poissonsche Integral / 444 \\
                 5. Die Maxwell--Sylvestersche Darstellung der
                 Kugelfunktionen / 445 \\
                 \S 6. Asymptotische Entwicklungen / 451 \\
                 1. Die Stirlingsche Formel / 452 \\
                 2. Asymptotische Berechnung der Hankeischen und
                 Besselschen Funktionen f{\"u}r gro{\ss}e Argumente /
                 453 \\
                 Sattelpunktmethode / 455 \\
                 4. Anwendung der Sattelpunktmethode zur Berechnung der
                 Hankeischen und Besselschen Funktionen bei gro{\ss}em
                 Parameter und gro{\ss}em Argument / 456 \\
                 5. Allgemeine Bemerkungen {\"u}ber die
                 Sattelpunktmethode / 460 \\
                 6. Methode von Darboux / 460 \\
                 7. Anwendung der Darbouxschen Methode zur
                 asymptotischen Entwicklung der Legendreschen Polynome /
                 461 \\
                 Sachverzeichnis / 463",
}

@Book{Courant:1968:MMPb,
  author =       "Richard Courant and David Hilbert",
  title =        "{Methoden der mathematischen Physik}. ({German})
                 [{Methods} of Mathematical Physics]",
  volume =       "2",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xvi + 549",
  year =         "1968",
  ISBN =         "0-387-04178-8, 3-540-04178-8",
  ISBN-13 =      "978-0-387-04178-0, 978-3-540-04178-8",
  LCCN =         "????",
  bibdate =      "Sun Nov 23 16:29:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Heidelberger Taschenb{\"u}cher (31)",
  acknowledgement = ack-nhfb,
  author-dates = "Richard Courant (1888--1972); David Hilbert
                 (1862--1943)",
  language =     "German",
  tableofcontents = "Erstes Kapitel \\
                 Vorbereitung. Grundbegriffe \\
                 \S 1. Orientierung {\"u}ber die Mannigfaltigkeit der
                 L{\"o}sungen / 2 \\
                 1. Beispiele / 2 \\
                 2. Differentialgleichungen zu gegebenen
                 Funktionenscharen und -familien / 7 \\
                 \S 2. Systeme von Differentialgleichungen / 10 \\
                 1. Problem der {\"A}quivalenz von Systemen und
                 einzelnen Differentialgleichungen / 10 \\
                 2. Bestimmte, {\"u}berbestimmte, unterbestimmte Systeme
                 / 12 \\
                 \S 3. Integrationsmethoden bei speziellen
                 Differentialgleichungen / 14 \\
                 1. Separation der Variablen / 14 \\
                 2. Erzeugung weiterer L{\"o}sungen durch Superposition.
                 Grundl{\"o}sung der W{\"a}rmeleitung. Poissons Integral
                 / 16 \\
                 \S 4. Geometrische Deutung einer partiellen
                 Differentialgleichung erster Ordnung mit zwei
                 unabh{\"a}ngigen Variablen. Das vollst{\"a}ndige
                 Integral / 18 \\
                 1. Die geometrische Deutung einer partiellen
                 Differentialgleichung erster Ordnung / 18 \\
                 2. Das vollst{\"a}ndige Integral / 19 \\
                 3. Singulare Integrale / 20 \\
                 \S 5. Theorie der linearen und quasilinearen
                 Differentialgleichungen erster Ordnung / 23 \\
                 1. Lineare Differentialgleichungen / 23 \\
                 2. Quasilineare Differentialgleichungen / 25 \\
                 \S 6. Die Legendresche Transformation / 26 \\
                 1. Legendresche Transformation f{\"u}r Funktionen von
                 zwei Ver{\"a}nderlichen / 26 \\
                 2. Die Legendresche Transformation f{\"u}r Funktionen
                 von $n$ Variablen / 28 \\
                 3. Anwendung der Legendreschen Transformation auf
                 partielle Differentialgleichungen / 29 \\
                 \S 7. Die Bestimmung der L{\"o}sungen durch ihre
                 Anfangswerte und der Existenzsatz / 31 \\
                 1. Formulierung und Erl{\"a}uterung des
                 Anfangswertproblems / 31 \\
                 2. Reduktion auf ein System von quasilinearen
                 Differentialgleichungen / 35 \\
                 3. Die Bestimmung der Ableitungen l{\"a}ngs der
                 Anfangsmannigfaltigkeit / 38 \\
                 4. Existenzbeweis analytischer L{\"o}sungen von
                 analytischen Differentialgleichungen / 39 \\
                 Anhang zum ersten Kapitel \\
                 \S 1. Die Differentialgleichung f{\"u}r die
                 St{\"u}tzfunktion einer Minimalfl{\"a}che / 44 \\
                 \S 2. Systeme von Differentialgleichungen erster
                 Ordnung und Differentialgleichungen h{\"o}herer Ordnung
                 / 46 \\
                 \S 3. Systeme von zwei partiellen
                 Differentialgleichungen erster Ordnung und
                 Differentialgleichungen zweiter Ordnung / 47 \\
                 \S 4. Darstellung der fl{\"a}chentreuen Abbildungen /
                 49 \\
                 Zweites Kapitel \\
                 Allgemeine Theorie der partiellen
                 Differentialgleichungen erster Ordnung \\
                 \S 1. Quasilineare Differentialgleichungen bei zwei
                 unabh{\"a}ngigen Ver{\"a}nderlichen / 51 \\
                 1. Charakteristische Kurven / 51 \\
                 2. Anfangswertproblem / 53 \\
                 3. Beispiele / 55 \\
                 \S 2. Quasilineare Differentialgleichungen bei n
                 unabh{\"a}ngigen Ver{\"a}nderlichen / 57 \\
                 \S 3. Allgemeine Differentialgleichungen mit zwei
                 unabh{\"a}ngigen Ver{\"a}nderlichen / 63 \\
                 1. Charakteristische Kurven und Fokalkurven / 63 \\
                 2. L{\"o}sung des Anfangswertproblems / 66 \\
                 3. Charakteristiken als Verzweigungselemente.
                 Erg{\"a}nzende Bemerkungen. Integralkonoid / 69 \\
                 \S 4. Zusammenhang mit der Theorie des
                 vollst{\"a}ndigen Integrals / 70 \\
                 \S 5. Fokalkurven und Mongesche Gleichung / 72 \\
                 \S 6. Beispiele / 74 \\
                 1. Die Differentialgleichung (gradw)2 = 1 / 74 \\
                 2. Zweites Beispiel / 77 \\
                 3. Die Differentialgleichung von Clairaut / 79 \\
                 4. Die Differentialgleichung der R{\"o}hrenfl{\"a}chen
                 / 80 \\
                 \S 7. Allgemeine Differentialgleichung mit n
                 unabh{\"a}ngigen Ver{\"a}nderlichen / 82 \\
                 \S 8. Vollst{\"a}ndiges Integral und
                 Hamilton-Jacobische Theorie / 87 \\
                 1. Enveloppenbildung und charakteristische Kurven / 87
                 \\
                 2. Die Kanonische Gestalt der charakteristischen
                 Differentialgleichungen / 89 \\
                 3. Hamilton-Jacobische Theorie / 90 \\
                 4. Beispiel. Zweik{\"o}rperproblem / 92 \\
                 5. Beispiel. Geod{\"a}tische Linien auf einem Ellipsoid
                 / 94 \\
                 \S 9. Hamiltonsche Theorie und Variationsrechnung / 96
                 \\
                 1. Die Eulerschen Differentialgleichungen in der
                 kanonischen Form / 96 \\
                 2. Der geod{\"a}tische Abstand oder das Eikonal, seine
                 Ableitungen und die Hamilton-Jacobische partielle
                 Differentialgleichung / 98 \\
                 3. Bemerkungen {\"u}ber den Fall homogener Integranden
                 / 100 \\
                 4. Extremalenfelder und Hamiltonsche
                 Differentialgleichung / 102 \\
                 5. Strahlenkegel. Huyghens Konstruktion / 105 \\
                 6. Huberts invariantes Integral zur Darstellung des
                 Eikonals / 105 \\
                 7. Der Satz von Hamilton und Jacobi / 107 \\
                 \S 10. Kanonische Transformationen und Anwendungen /
                 107 \\
                 1. Die kanonische Transformation / 107 \\
                 2. Neuer Beweis des Hamilton-Jacobischen Satzes / 109
                 \\
                 3. Variation der Konstanten (kanonische
                 St{\"o}rungstheorie) / 110 \\
                 Anhang zum zweiten Kapitel \\
                 \S 1. Erneute Diskussion der charakteristischen
                 Mannigfaltigkeiten / 110 \\
                 1. Formale Vorbemerkungen zur Differentiation in $n$
                 Dimensionen / 111 \\
                 2. Anfangswertproblem und charakteristische
                 Mannigfaltigkeiten / 113 \\
                 \S 2. Systeme quasilinearer Differentialgleichungen mit
                 gleichem Hauptteil. Neue Herleitung der
                 Charakteristikentheorie / 117 \\
                 Literatur zum ersten und zweiten Kapitel / 122 \\
                 Drittes Kapitel \\
                 Lineare Differentialgleichungen h{\"o}herer Ordnung im
                 allgemeinen \\
                 1. Normalformen bei linearen
                 Differentialgleichungsausdr{\"u}cken zweiter Ordnung
                 mit zwei unabh{\"a}ngigen Ver{\"a}nderlichen / 123 \\
                 1. Elliptische, hyperbolische, parabolische
                 Normalformen / 123 \\
                 2. Beispiele / 128 \\
                 2. Normalformen quasilinearer Differentialgleichungen /
                 130 \\
                 1. Normalformen / 130 \\
                 2. Beispiel. Minimalfl{\"a}chen / 133 \\
                 \S 3. Klasseneinteilung der linearen
                 Differentialgleichungen zweiter Ordnung bei mehr
                 unabh{\"a}ngigen Ver{\"a}nderlichen / 135 \\
                 1. Elliptische, hyperbolische und parabolische
                 Differentialgleichungen / 135 \\
                 2. Lineare Differentialgleichungen zweiter Ordnung mit
                 konstanten Koeffizienten / 137 \\
                 \S 4. Differentialgleichungen h{\"o}herer Ordnung und
                 Systeme von Differentialgleichungen 138 \\
                 1. Differentialgleichungen h{\"o}herer Ordnung / 138
                 \\
                 2. Typeneinteilung bei Systemen von
                 Differentialgleichungen / 141 \\
                 3. Bemerkungen {\"u}ber nichtlineare Probleme / 146 \\
                 \S 5. Lineare Differentialgleichungen mit konstanten
                 Koeffizienten / 146 \\
                 1. Allgemeines / 146 \\
                 2. Ebene Wellen. Verzerrungsfreiheit. Dispersion / 147
                 \\
                 3. Beispiele: Telegraphengleichung, Verzerrungsfreiheit
                 bei Kabeln / 152 \\
                 4. Zylinder- und Kugelwellen / 153 \\
                 \S 6. Anfangswertprobleme, Ausstrahlungsprobleme / 156
                 \\
                 1. Anfangswertprobleme der W{\"a}rmeleitung.
                 Transformation der ^-Funktion / 156 \\
                 2. Anfangswertprobleme der Wellengleichung / 159 \\
                 3. Methode des Fourierschen Integrals zur L{\"o}sung
                 von Anfangswertproblemen / 160 \\
                 4. L{\"o}sung der unhomogenen Gleichung durch Variation
                 der Konstanten. Retardierte Potentiale / 164 \\
                 5. Das Anfangswertproblem f{\"u}r die Wellengleichung
                 in zwei Raumdimensionen. Absteigemethode / 166 \\
                 6. Das Ausstral lungsproblem / 167 \\
                 \S 7. Ausbreitungsvorg{\"a}nge und Huyghenssches
                 Prinzip / 169 \\
                 7. Die typischen Differentialgleichungsprobleme der
                 mathematischen Physik / 171 \\
                 1. Vorbemerkungen. Beispiele typischer
                 Problemstellungen 171 \\
                 2. Grunds{\"a}tzliche Betrachtungen / 175 \\
                 Anhang zum dritten Kapitel. Ausgleichsprobleme und
                 Heavisides Operatorenkalk{\"u}l / 179 \\
                 \S 1. Ausgleichsprobleme und, L{\"o}sung mittels
                 Integraldarstellungen / 180 \\
                 1. Beispiel. Wellengleichung / 180 \\
                 2. Allgemeine Problemstellung / 182 \\
                 3. Integral von Duhamel / 183 \\
                 4. Methode der Superposition von
                 Exponentiall{\"o}sungen / 185 \\
                 \S 2. Die Heavisidesche Operatorenmethode / 187 \\
                 1. Die einfachsten Operatoren / 187 \\
                 2. Beispiele / 190 \\
                 3. Anwendungen auf Ausgleichsprobleme / 194 \\
                 4. Wellengleichung / 195 \\
                 5. Methode zur Rechtfertigung des
                 Operatorenkalk{\"u}ls. Realisierung weiterer Operatoren
                 / 196 \\
                 \S 3. Zur allgemeinen Theorie der Ausgleichsprobleme /
                 202 \\
                 1. Die Transformation von Laplace / 202 \\
                 2. L{\"o}sung der Ausgleichsprobleme mit Hilfe der
                 Laplaceschen Transformation / 205 \\
                 3. Beispiele / 210 \\
                 Literatur zum Anhang des dritten Kapitels / 222 \\
                 Viertes Kapitel \\
                 Elliptische Differentialgleichungen, insbesondere
                 Potentialtheorie \\
                 \S 1. Vorbemerkungen / 223 \\
                 1. Die Differentialgleichungen von Laplace, Poisson und
                 verwandte Differentialgleichungen / 223 \\
                 2. Potentiale von Massenbelegungen / 227 \\
                 3. Greensche Formeln und Anwendungen / 231 \\
                 4. Die Ableitungen der Belegungspotentiale / 236 \\
                 \S 2. Poissons Integral und Folgerungen / 239 \\
                 1. Randwertaufgabe und Greensche Funktion / 239 \\
                 2. Greensche Funktion f{\"u}r Kreis und Kugel. Das
                 Poissonsche Integral f{\"u}r Kugel und Halbraum / 241
                 \\
                 3. Folgerungen aus der Poissonschen Formel / 245 \\
                 \S 3. Der Mittelwertsatz und Anwendungen / 249 \\
                 1. Homogene und unhomogene Mittelwertgleichung / 249
                 \\
                 2. Umkehrung der Mittelwerts{\"a}tze / 251 \\
                 3. Die Poissonsche Gleichung f{\"u}r Potentiale von
                 Raumbelegungen / 257 \\
                 4. Mittelwerts{\"a}tze f{\"u}r andere elliptische
                 Differentialgleichungen / 258 \\
                 \S 4. Die Randwertaufgabe / 262 \\
                 1. Vorbemerkungen. Stetige Abh{\"a}ngigkeit von den
                 Randwerten und vom Gebiet / 262 \\
                 2. L{\"o}sung der Randwertaufgabe mit Hilfe des
                 alternierenden Verfahrens / 264 \\
                 3. Die Integralgleichungsmethode f{\"u}r Gebiete mit
                 hinreichend glatten R{\"a}ndern / 269 \\
                 4. Weitere Bemerkungen zur Randwertaufgabe / 272 \\
                 \S 5. Randwertaufgaben f{\"u}r allgemeinere elliptische
                 Differentialgleichungen; eindeutige Bestimmtheit der
                 L{\"o}sungen / 274 \\
                 1. Lineare Differentialgleichungen / 274 \\
                 2. Quasilineare Differentialgleichungen / 276 \\
                 3. Ein Satz von Rellich {\"u}ber die
                 Differentialgleichung von Monge-Amp{\`e}re / 277 \\
                 \S 6. Die Integralgleichungsmethode zur L{\"o}sung
                 elliptischer Differentialgleichungen / 279 \\
                 1. Konstruktion von L{\"o}sungen {\"u}berhaupt.
                 Grundl{\"o}sungen / 279 \\
                 2. Die Randwertaufgabe / 282 \\
                 Anhang zum vierten Kapitel \\
                 1. Verallgemeinerung der Randwertaufgabe. S{\"a}tze von
                 Wiener / 284 \\
                 2. Nichtlineare Differentialgleichungen / 286 \\
                 Lehrbuchliteratur zum vierten Kapitel / 289 \\
                 F{\"u}nftes Kapitel \\
                 Hyperbolische Differentialgleichungen mit zwei
                 unabh{\"a}ngigen Ver{\"a}nderlichen \\
                 \S 1. Die Charakteristiken bei quasilinearen
                 Differentialgleichungen / 291 \\
                 1. Definition der Charakteristiken / 291 \\
                 2. Charakteristiken auf Integralfl{\"a}chen / 296 \\
                 3. Charakteristiken als Unstetigkeitslinien.
                 Wellenfronten / 297 \\
                 \S 2. Charakteristiken f{\"u}r allgemeine
                 Differentialgleichungsprobleme / 299 \\
                 1. Allgemeine Differentialgleichungen zweiter Ordnung /
                 299 \\
                 2. Differentialgleichungen h{\"o}herer Ordnung / 301
                 \\
                 3. Systeme von Differentialgleichungen / 303 \\
                 4. Invarianz der Charakteristiken gegen{\"u}ber
                 beliebigen Punkttransformationen / 304 \\
                 5. Beispiele aus der Hydrodynamik / 305 \\
                 \S 3. Eindeutigkeit und Abh{\"a}ngigkeitsgebiet / 307
                 \\
                 1. Grunds{\"a}tzliches {\"u}ber
                 Ausbreitungsvorg{\"a}nge / 307 \\
                 2. Eindeutigkeitsbeweise / 308 \\
                 \S 4. Die Riemannsche Integrationsmethode / 311 \\
                 1. Riemanns Darstellungsformel / 311 \\
                 2. Erg{\"a}nzende Bemerkungen / 315 \\
                 3. Beispiel, Telegraphengleichung / 316 \\
                 \S 5. Die L{\"o}sungen der Differentialgleichung $u_{x
                 y} = f(x, y, u, u_x, u_y)$ nach dem Picardschen
                 Iterationsverfahren / 317 \\
                 1. Vorbemerkungen / 317 \\
                 2. L{\"o}sung der Anfangswertprobleme / 319 \\
                 3. Eindeutige Bestimmtheit der L{\"o}sung / 321 \\
                 4. Stetige und differenzierbare Abh{\"a}ngigkeit von
                 Parametern / 322 \\
                 5. Das Abh{\"a}ngigkeitsgebiet der L{\"o}sung / 323 \\
                 \S 6. Verallgemeinerungen und Anwendung auf Systeme
                 erster Ordnung / 323 \\
                 1. Systeme von Differentialgleichungen zweiter Ordnung
                 mit gleichem linearen Hauptteil / 323 \\
                 2. Kanonisch-hyperbolische Systeme erster Ordnung / 324
                 \\
                 \S 7. Die allgemeine quasilineare Gleichung zweiter
                 Ordnung / 326 \\
                 1. Das vollst{\"a}ndige System der charakteristischen
                 Differentialgleichungen / 326 \\
                 2. L{\"o}sung des Anfangswertproblems / 330 \\
                 \S 8. Die allgemeine Gleichung $F(x, y, u, p, q, r, s,
                 t) = 0$ / 332 \\
                 1. Quasilineare Systeme mit gleichem Hauptteil / 333
                 \\
                 2. L{\"o}sung des Anfangswertproblems im allgemeinen
                 Fall / 333 \\
                 Anhang zum f{\"u}nften Kapitel \\
                 \S 1. Einf{\"u}hrung komplexer Gr{\"o}{\ss}en.
                 {\"U}bergang vom hyperbolischen zum elliptischen Fall
                 durch komplexe Variable / 337 \\
                 \S 2. Der analytische Charakter der L{\"o}sungen im
                 elliptischen Fall / 338 \\
                 1. Funktionentheoretische Vorbemerkung / 338 \\
                 2. Analytischer Charakter der L{\"o}sungen von Au =
                 f(x,y,u,p,q) / 339 \\
                 3. Bemerkung {\"u}ber den allgemeinen Fall / 342 \\
                 \S 3. Weitere Bemerkungen zur Charakteristikentheorie
                 bei zwei Ver{\"a}nderlichen / 343 \\
                 \S 4. Sonderstellung der Monge-Ampereschen Gleichungen
                 / 344 \\
                 Sechstes Kapitel \\
                 Hyperbolische Differentialgleichungen mit mehr als zwei
                 unabh{\"a}ngigen Ver{\"a}nderlichen \\
                 \S 1. Die charakteristische Gleichung / 346 \\
                 1. Quasilineare Differentialgleichungen zweiter Ordnung
                 / 346 \\
                 2. Lineare Differentialgleichungen. Charakteristische
                 Strahlen / 350 \\
                 \S 2. Charakteristische Mannigfaltigkeiten als
                 Unstetigkeitsflachen von L{\"o}sungen. Wellenfronten /
                 356 \\
                 1. Unstetigkeiten zweiter Ordnung / 356 \\
                 2. Wellenfronten bei linearen Differentialgleichungen
                 als Tr{\"a}ger h{\"o}herer Unstetigkeiten / 359 \\
                 3. Die Differentialgleichung l{\"a}ngs einer
                 charakteristischen Mannigfaltigkeit. Ausbreitung der
                 Unstetigkeiten l{\"a}ngs der Strahlen / 362 \\
                 4. Physikalische Deutung. Schattengrenzen / 364 \\
                 5. Strahlenkonoid. Zusammenhang mit der Riemannschen
                 Ma{\ss}bestimmung / 365 \\
                 6. Die Huygensche Konstruktion der Wellenfronten.
                 Strahlenkegel und Richtungsausbreitung / 367 \\
                 7. Strahlen- und Normalenkegel / 368 \\
                 8. Beispiel. Die Poissonsche Wellengleichung in drei
                 Raumdimensionen / 370 \\
                 \S 3. Charakteristiken bei Problemen h{\"o}herer
                 Ordnung / 372 \\
                 1. Lineare Differentialgleichungen h{\"o}herer Ordnung
                 / 372 \\
                 2. Systeme von Differentialgleichungen. Hydrodynamik /
                 374 \\
                 3. Weitere Systeme. Krystalloptik / 376 \\
                 \S 4. Eindeutigkeitss{\"a}tze und
                 Abh{\"a}ngigkeitsgebiet bei Anfangswertproblemen / 379
                 \\
                 1. Die Wellengleichung / 379 \\
                 2. Die Differentialgleichung $u_{t t} - \Delta u +
                 \frac{\lambda}{t} u_t = 0$ (Darboux) / 381 \\
                 3. Maxwellsche Gleichungen im {\"A}ther / 382 \\
                 4. Eindeutigkeit und Abh{\"a}ngigkeitsgebiet bei den
                 Differentialgleichungen der Krystalloptik / 383 \\
                 5. Bemerkungen {\"u}ber Abh{\"a}ngigkeits- und
                 Wirkungsgebiete. Notwendigkeit des konvexen Charakters
                 von Abh{\"a}ngigkeitsgebieten / 385 \\
                 \S 5. Hyperbolische lineare Differentialgleichungen
                 zweiter Ordnung mit konstanten Koeffizienten / 385 \\
                 1. Konstruktion der L{\"o}sung / 387 \\
                 2. Bemerkungen {\"u}ber die Absteigemethode / 391 \\
                 3. N{\"a}here Diskussion der L{\"o}sungen. Prinzip von
                 Huyghens / 393 \\
                 4. Verifikation der L{\"o}sung / 398 \\
                 5. Integration der unhomogenen Gleichung / 401 \\
                 6. Das Ausstrahlungsproblem / 403 \\
                 7. Das Anfangswertproblem f{\"u}r die Gleichung Au +
                 c2u = utt und f{\"u}r die Telegraphengleichung / 408
                 \\
                 \S 6. Mittelwertmethode. Wellengleichung und Gleichung
                 von Darboux / 411 \\
                 1. Die Darbouxsche Differentialgleichung f{\"u}r
                 Mittelwerte / 411 \\
                 2. Zusammenhang mit der Wellengleichung und
                 Aufl{\"o}sung der Wellengleichung / 412 \\
                 3. Das Ausstrahlungsproblem der Wellengleichung / 415
                 \\
                 4. Ein Satz von Friedrichs / 416 \\
                 \S 7. Ultrahyperbolische Differentialgleichungen und
                 allgemeine Differentialgleichungen zweiter Ordnung mit
                 konstanten Koeffizienten, / 417 \\
                 1. Der allgemeine Mittelwertsatz von Asgeirsson / 417
                 \\
                 2. Anderer Beweis des Mittelwertsatzes / 420 \\
                 3. Anwendung des Mittelwertsatzes auf die
                 Wellengleichung / 420 \\
                 4. L{\"o}sungen des charakteristischen
                 Anfangswertproblems der Wellengleichung / 421 \\
                 5. Andere Anwendungen des Mittelwertsatzes / 423 \\
                 \S 8. Betrachtungen {\"u}ber nichthyperbolische
                 Anfangswertprobleme / 425 \\
                 1. Bestimmung einer Funktion aus gewissen
                 Kugelmittelwerten / 425 \\
                 2. Anwendungen auf das Anfangswertproblem / 427 \\
                 \S 9. Die Methode von Hadamard zur L{\"o}sung des
                 Anfangswertproblems / 430 \\
                 1. Vorbemerkungen. Grundl{\"o}sung. Allgemeine Methode
                 / 431 \\
                 2. Die allgemeine Wellengleichung in $m = 2$
                 Raumdimensionen / 438 \\
                 2. Die verallgemeinerte Wellengleichung in $m = 3$
                 Raumdimensionen / 443 \\
                 \S 10. Bemerkungen {\"u}ber den Wellenbegriff und das
                 Ausstrahlungsproblem / 448 \\
                 1. Allgemeines. Verzerrungsfreie fortschreitende Wellen
                 / 448 \\
                 2. Sph{\"a}rische Wellen / 451 \\
                 3. Ausstrahlung und Huygenssches Prinzip / 453 \\
                 Anhang zum sechsten Kapitel \\
                 \S 1. Die Differentialgleichungen der Krystalloptik /
                 455 \\
                 1. Normalen- und Strahlenfl{\"a}che der Krystalloptik /
                 455 \\
                 2. Gestalt der Normalenfl{\"a}che / 455 \\
                 3. Die Strahlenfl{\"a}che / 458 \\
                 4. Reduktion des Differentialgleichungssystems auf eine
                 Differentialgleichung sechster Ordnung bzw. vierter
                 Ordnung / 460 \\
                 5. Explizite L{\"o}sung durch die Fouriersche Methode /
                 462 \\
                 6. Diskussion des l{\"o}senden Kernes $K$ / 462 \\
                 7. Optische Anwendung. Konische Refraktion / 465 \\
                 \S 2. Abh{\"a}ngigkeitsgebiete bei Problemen
                 h{\"o}herer Ordnung / 465 \\
                 \S 3. Huyghens Prinzip im weiteren Sinne und
                 fortsetzbare Anfangsbedingungen / 468 \\
                 \S 4. Ersetzung von Differentialgleichungen durch
                 Integralrelationen. Erweiterung des
                 Charakteristikenbegriffes / 469 \\
                 Siebentes Kapitel \\
                 L{\"o}sung der Rand- und Eigenwertprobleme auf Grund
                 der Variationsrechnung \\
                 \S 1. Vorbereitungen / 473 \\
                 1. Das Dirichletsche Prinzip f{\"u}r den Kreis / 473
                 \\
                 2. Allgemeine Problemstellungen / 476 \\
                 3. Lineare Funktionenr{\"a}ume mit quadratischer
                 Metrik. Definitionen / 478 \\
                 4. Randbedingungen / 482 \\
                 \S 2. Die erste Randwertaufgabe / 483 \\
                 1. Problemstellung / 483 \\
                 2. Greensche Formel. Hauptungleichung zwischen $D$ und
                 $H$. Eindeutigkeit / 484 \\
                 3. Minimalfolgen und L{\"o}sung des Randwertproblems /
                 486 \\
                 \S 3. Das Eigenwertproblem bei verschwindenden
                 Randwerten / 488 \\
                 1. Integralungleichungen / 488 \\
                 2. Das erste Eigenwertproblem 5 \\
                 490 \\
                 3. H{\"o}here Eigenwerte und -funktionen.
                 Vollst{\"a}ndigkeit / 492 \\
                 \S 4. Annahme der Randwerte bei zwei unabh{\"a}ngigen
                 Ver{\"a}nderlichen / 495 \\
                 \S 5. Konstruktion der Grenzfunktionen und
                 Konvergenzeigenschaften der Integrale $E$, $D$, $H$ /
                 497 \\
                 1. Konstruktion der Grenzfunktionen / 497 \\
                 2. Konvergenzeigenschaften der Integrale $D$ und $H$ /
                 504 \\
                 \S 6. Zweite und dritte Randbedingung. Randwertaufgabe
                 / 508 \\
                 1. Greensche Formel und Randbedingungen / 508 \\
                 2. Formulierung des Randwertproblems und
                 Variationsproblems / 509 \\
                 3. Einschr{\"a}nkung der Klasse zul{\"a}ssiger Gebiete
                 / 511 \\
                 4. {\"A}quivalenz von Minimumproblem und
                 Randwertproblem. Eindeutigkeit / 512 \\
                 5. L{\"o}sung des Variationsproblems und
                 Randwertproblems / 512 \\
                 \S 7. Das Eigenwertproblem bei zweiter und dritter
                 Randwertbildung / 513 \\
                 \S 8. Diskussion der bei der zweiten und dritten
                 Randbedingung zugrunde gelegten Gebiete / 515 \\
                 1. Gebiete vom Typus 9J / 515 \\
                 2. Notwendigkeit von einschr{\"a}nkenden Bedingungen
                 f{\"u}r das Gebiet / 521 \\
                 \S 9. Erg{\"a}nzungen und Aufgaben ' / 523 \\
                 1. Die Greensche Funktion von $\Delta u$ / 523 \\
                 2. Dipolsingularit{\"a}t / 525 \\
                 3. Randverhalten bei $\Delta u = 0$ und zwei
                 unabh{\"a}ngigen Ver{\"a}nderlichen f{\"u}r die zweite
                 Randbedingung / 526 \\
                 4. Stetige Abh{\"a}ngigkeit vom Gebiet / 526 \\
                 5. {\"U}bertragung der Theorie auf unendlich
                 ausgedehnte Gebiete $G$ / 527 \\
                 6. Anwendung der Methode auf Differentialgleichungen
                 vierter Ordnung. Transversaldeformation und
                 Schwingungen von Platten / 528 \\
                 7. Erste Randwert- und Eigenwertaufgabe der
                 Elastizit{\"a}tstheorie bei zwei Dimensionen / 530 \\
                 8. Andere Methode zur Konstruktion der Grenzfunktion /
                 532 \\
                 \S 10. Das Problem von Plateau / 535 \\
                 1. Problemstellung und Ansatz zur L{\"o}sung / 535 \\
                 2. Beweis der Variationsrelationen / 538 \\
                 3. Existenz der L{\"o}sung des Variationsproblems / 541
                 \\
                 Erg{\"a}nzende Literaturangaben / 544 \\
                 Namen- und Sachverzeichnis / 545",
}

@Book{Courant:1989:MMPa,
  author =       "Richard Courant and David Hilbert",
  title =        "Methods of Mathematical Physics",
  volume =       "1",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 560",
  year =         "1989",
  DOI =          "https://doi.org/10.1002/9783527617210",
  ISBN =         "0-471-50447-5, 3-527-61721-3 (e-book)",
  ISBN-13 =      "978-0-471-50447-4, 978-3-527-61721-0 (e-book)",
  LCCN =         "QA401 .C72413 1989",
  MRclass =      "00A69, 15-01, 33-01, 34-01, 35-01, 45-01, 49-01",
  bibdate =      "Sun Nov 23 16:06:11 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Wiley classics library",
  URL =          "http://onlinelibrary.wiley.com/book/10.1002/9783527617210;
                 http://www.gbv.de/dms/bowker/toc/9780471504474.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0729.00007",
  ZMnumber =     "0729.00007",
  acknowledgement = ack-nhfb,
  author-dates = "Richard Courant (1888--1972); David Hilbert
                 (1862--1943)",
  tableofcontents = "Frontmater / i--xv \\
                 1: The Algebra of Linear Transformations and Quadratic
                 Forms / 1--47 \\
                 Transformation to Principal Axes of Quadratic and
                 Hermitian Forms \\
                 Minimum--Maximum Property of Eigenvalues \\
                 2: Series Expansion of Arbitrary Functions / 48--11 \\
                 Orthogonal Systems of Functions \\
                 Measure of Independence and Dimension Number \\
                 Fourier Series \\
                 Legendre Polynomials \\
                 3: Linear Integral Equations / 112--163 \\
                 The Expansion Theorem and Its Applications \\
                 Neumann Series and the Reciprocal Kernel \\
                 The Fredholm Formulas \\
                 4: The Calculus of Variations / 164--274 \\
                 Direct Solutions \\
                 The Euler Equations \\
                 5: Vibration and Eigenvalue Problems / 275--396 \\
                 Systems of a Finite Number of Degrees of Freedom \\
                 The Vibrating String \\
                 The Vibrating Membrane \\
                 Green's Function (Influence Function) and Reduction of
                 Differential Equations to Integral Equations \\
                 6: Application of the Calculus of Variations To
                 Eigenvalue Problems / 397--465 \\
                 Completeness and Expansion Theorems \\
                 Nodes of Eigenfunctions \\
                 7: Special Functions Defined By Eigenvalue Problems /
                 466--545 \\
                 Bessel Functions \\
                 Asymptotic Expansions \\
                 Additional Bibliography / 546--549 \\
                 Index / 551--560",
}

@Book{Courant:1989:MMPb,
  author =       "Richard Courant",
  title =        "Methods of Mathematical Physics: Partial Differential
                 Equations",
  volume =       "2",
  publisher =    "Interscience Publishers",
  address =      "New York, NY, USA",
  pages =        "xxii + 830",
  year =         "1989",
  DOI =          "https://doi.org/10.1002/9783527617234",
  ISBN =         "0-471-50439-4 (vol. 2)",
  ISBN-13 =      "978-0-471-50439-9 (vol. 2)",
  LCCN =         "QA401 .C72413 1989",
  bibdate =      "Sat Nov 22 18:27:34 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley classics library",
  URL =          "http://onlinelibrary.wiley.com/book/10.1002/9783527617234;
                 http://www.loc.gov/catdir/enhancements/fy0607/89112829-b.html;
                 http://www.loc.gov/catdir/enhancements/fy0607/89112829-d.html;
                 http://www.loc.gov/catdir/toc/onix05/89112829.html",
  acknowledgement = ack-nhfb,
  author-dates = "Richard Courant (1888--1972)",
  remark =       "Translation of \booktitle{Methoden der mathematischen
                 Physik}.",
  subject =      "Mathematical physics",
  tableofcontents = "Frontmatter / i--xxii \\
                 1: Introductory Remarks / 1--61 \\
                 2: General Theory of Partial Differential Equations of
                 First Order / 62--131 \\
                 3: Differential Equations of Higher Order / 154--239
                 \\
                 4: Potential Theory and Elliptic Differential Equations
                 / 240--406 \\
                 5: Hyperbolic Differential Equations in Two Independent
                 Variables / 407--550 \\
                 6: Hyperbolic Differential Equations in More Than Two
                 Independent Variables / 551--798 \\
                 Bibliography / 799--818 \\
                 Index / 819--830",
}

@Book{Crilly:2006:ACM,
  author =       "A. J. (Tony) Crilly",
  title =        "{Arthur Cayley}: Mathematician Laureate of the
                 {Victorian} Age",
  publisher =    pub-JOHNS-HOPKINS,
  address =      pub-JOHNS-HOPKINS:adr,
  pages =        "xxiv + 610",
  year =         "2006",
  ISBN =         "0-8018-8011-4",
  ISBN-13 =      "978-0-8018-8011-7",
  LCCN =         "QA29 .C39 C75 2006",
  MRclass =      "01A70 (01A55)",
  MRnumber =     "2284396 (2008d:01016)",
  MRreviewer =   "Karl-Heinz Schlote",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/magma.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/bios/jhu052/2004005682.html;
                 http://www.loc.gov/catdir/description/jhu051/2004005682.html;
                 http://www.loc.gov/catdir/toc/fy0612/2004005682.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Cayley, Arthur; Mathematicians; Great Britain;
                 Biography",
  subject-dates = "1821--1895",
  tableofcontents = "Part 1 \\
                 Growing Up, 1821--1843 / 1 \\
                 1: Early Years / 3 \\
                 2: A Cambridge Prodigy / 27 \\
                 3: Coming of Age / 57 \\
                 Part 2 \\
                 New Vistas, 1844--1849 / 79 \\
                 4: A Mathematical Medley / 81 \\
                 5: From a Fenland Base / 101 \\
                 6: The Pupil Barrister / 120 \\
                 Part 3 \\
                 A Rising Star, 1850--1862 / 155 \\
                 7: Barrister-at-Law / 157 \\
                 8: A Grand Design / 184 \\
                 9: Without Portfolio / 214 \\
                 10: The Road to Academe / 235 \\
                 Part 4 \\
                 The High Plateau, 1863--1882 / 259 \\
                 11: The Mathematician Laureate / 261 \\
                 12: Years of Challenge / 290 \\
                 13: A Representative Man / 312 \\
                 14: March On with Step Sublime / 341 \\
                 Part 5 \\
                 Make One Music as Before, 1882--1895 / 369 \\
                 15: ``A Tract of Beautiful Country'' / 371 \\
                 16: The Old Man of Mathematics / 390 \\
                 17: Last Years / 417 \\
                 Appendix A: Arthur Cayley's Social Circle / 443 \\
                 Appendix B: Glossary of Mathematical Terms / 468 \\
                 Abbreviations / 477 \\
                 Notes / 483 \\
                 Bibliography / 559 \\
                 Index",
  xxauthor =     "Tony Crilly",
  xxpages =      "xxi + 609",
}

@Book{Cullen:1966:MLT,
  author =       "Charles G. Cullen",
  title =        "Matrices and Linear Transformations",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "viii + 227",
  year =         "1966",
  LCCN =         "QA263 .C8",
  MRclass =      "15.00",
  MRnumber =     "0197472 (33 \#5637)",
  MRreviewer =   "M. Pearl",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Cullen:1972:MLT,
  author =       "Charles G. Cullen",
  title =        "Matrices and Linear Transformations",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xii + 318",
  year =         "1972",
  ISBN =         "0-201-01209-X",
  ISBN-13 =      "978-0-201-01209-5",
  LCCN =         "QA263 .C8 1972",
  bibdate =      "Sat Nov 22 18:28:44 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Addison-Wesley series in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Matrices; Transformations (Mathematics)",
}

@Book{Cullen:1990:MLT,
  author =       "Charles G. Cullen",
  title =        "Matrices and Linear Transformations",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second",
  pages =        "xii + 318",
  year =         "1990",
  ISBN =         "0-486-66328-0",
  ISBN-13 =      "978-0-486-66328-9",
  LCCN =         "QA188 .C85 1990",
  bibdate =      "Sat Nov 22 18:28:44 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/89025677.html;
                 http://www.loc.gov/catdir/enhancements/fy1318/89025677-t.html",
  acknowledgement = ack-nhfb,
  remark =       "An unabridged, corrected republication of the second
                 edition (1972) of the work originally published in 1966
                 by Addison-Wesley Publishing Company.",
  subject =      "Matrices; Transformations (Mathematics)",
}

@Book{Donoghue:1974:MMF,
  author =       "William F. (William Francis) {Donoghue, Jr.}",
  title =        "Monotone Matrix Functions and Analytic Continuation",
  volume =       "207",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "v + 182",
  year =         "1974",
  ISBN =         "0-387-06543-1",
  ISBN-13 =      "978-0-387-06543-4",
  LCCN =         "QA331 .D687",
  MRclass =      "30A96 (30A14 30A30 47A10)",
  MRnumber =     "0486556 (58 \#6279)",
  MRreviewer =   "Harkrishan Vasudeva",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Die Grundlehren der mathematischen Wissenschaften in
                 Einzeldarstellungen mit besonderer Ber{\"u}cksichtigung
                 der Anwendungsgebeite",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Faddeeva:1959:CML,
  author =       "V. N. Faddeeva",
  title =        "Computational Methods of Linear Algebra",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 252",
  year =         "1959",
  LCCN =         "QA251 .F313",
  MRclass =      "65.00",
  MRnumber =     "0100344 (20 \#6777)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  remark =       "Translated from the Russian by C. D. Benster.",
  subject =      "Algebras, Linear; Matrices; Numerical calculations",
}

@Book{Faddeev:1963:CML,
  author =       "D. K. (Dmitri{\u{\i}} Konstantinovich) Faddeev and V.
                 N. Faddeeva",
  title =        "Computational Methods of Linear Algebra",
  publisher =    pub-W-H-FREEMAN,
  address =      pub-W-H-FREEMAN:adr,
  pages =        "xi + 621",
  year =         "1963",
  LCCN =         "QA251 .F283",
  bibdate =      "Sun Nov 23 07:37:15 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "A Series of undergraduate books in mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Translation by Robert C. Williams of
                 \booktitle{Vychislitel'nye metody line{\u{\i}}noi
                 algebry}.",
  subject =      "Algebras, Linear",
}

@Book{Fallat:2011:TNM,
  author =       "Shaun M. Fallat and Charles R. Johnson",
  title =        "Totally Nonnegative Matrices",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xv + 248",
  year =         "2011",
  ISBN =         "0-691-12157-5 (hardcover), 1-4008-3901-7 (e-book)",
  ISBN-13 =      "978-0-691-12157-4 (hardcover), 978-1-4008-3901-8
                 (e-book)",
  LCCN =         "QA188 .F35 2011",
  MRclass =      "15-02 (15B48)",
  MRnumber =     "2791531 (2012d:15001)",
  MRreviewer =   "Juan Manuel Pe{\~n}a",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2010.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Princeton Series in Applied Mathematics",
  URL =          "http://www.jstor.org/stable/10.2307/j.ctt7scff",
  abstract =     "Totally nonnegative matrices arise in a remarkable
                 variety of mathematical applications. This book is a
                 comprehensive and self-contained study of the essential
                 theory of totally nonnegative matrices, defined by the
                 nonnegativity of all subdeterminants. It explores
                 methodological background, historical highlights of key
                 ideas, and specialized topics.The book uses classical
                 and ad hoc tools, but a unifying theme is the
                 elementary bidiagonal factorization, which has emerged
                 as the single most important tool for this particular
                 class of matrices. Recent work has shown that
                 bidiagonal factorizations may be viewed in a succinct
                 combinatorial way, leading to many deep insights.
                 Despite slow development, bidiagonal factorizations,
                 along with determinants, now provide the dominant
                 methodology for understanding total nonnegativity. The
                 remainder of the book treats important topics, such as
                 recognition of totally nonnegative or totally positive
                 matrices, variation diminution, spectral properties,
                 determinantal inequalities, Hadamard products, and
                 completion problems associated with totally nonnegative
                 or totally positive matrices. The book also contains
                 sample applications, an up-to-date bibliography, a
                 glossary of all symbols used, an index, and related
                 references.\par

                 \booktitle{Totally Nonnegative Matrices} is a
                 comprehensive, modern treatment of the titled class of
                 matrices that arise in very many ways. Methodological
                 background is given, and elementary bidiagonal
                 factorization is a featured tool. In addition to
                 historical highlights and sources of interest, some of
                 the major topics include: recognition, variation
                 diminution, spectral structure, determinantal
                 inequalities, Hadamard products, and completion
                 problems.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "non-negative matrices; mathematics / applied;
                 mathematics / matrices; mathematics / algebra /
                 linear",
}

@Book{Fan:1959:CST,
  author =       "Ky Fan",
  title =        "Convex Sets and Their Applications [lecture notes]",
  publisher =    "Applied Mathematics Division, Argonne National
                 Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "????",
  year =         "1959",
  LCCN =         "????",
  bibdate =      "Fri Nov 21 08:31:45 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  remark =       "I am unable to find this report online, even at
                 anl.gov, although there are many references to it.",
}

@TechReport{Fiedler:1975:SPS,
  author =       "Miroslav Fiedler",
  title =        "Spectral Properties of Some Classes of Matrices",
  type =         "Lecture Notes",
  number =       "75.01R",
  institution =  "Chalmers University of Technology and the University
                 of G{\"o}teborg",
  address =      "G{\"o}teborg, Sweden",
  pages =        "????",
  year =         "1975",
  bibdate =      "Fri Nov 21 08:35:49 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  remark =       "I am unable to find this report online, even at the
                 author's Web site, and there are few references to
                 it.",
}

@Book{Fiedler:1986:SMT,
  author =       "Miroslav Fiedler",
  title =        "Special Matrices and Their Applications in Numerical
                 Mathematics",
  publisher =    "Martinus Nijhoff Publishers",
  address =      "Dordrecht, The Netherlands",
  pages =        "xi + 307",
  year =         "1986",
  DOI =          "https://doi.org/10.1007/978-94-009-4335-3",
  ISBN =         "90-247-2957-2",
  ISBN-13 =      "978-90-247-2957-9",
  LCCN =         "QA188 .F5313 1986",
  MRclass =      "15-02 (65Fxx)",
  MRnumber =     "1105955 (92b:15003)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Translated from the Czech \booktitle{Speci{\'a}ln{\'i}
                 matice a jejich pou{\v{z}}it{\'i} v numerick{\'e}
                 matematice} by Petr P{\v{r}}ikryl and Karel Segeth.",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002867827.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0677.65019",
  ZMnumber =     "0677.65019",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  mynote =       "Nothing original or unusual here. Little on test
                 matrices. More just a mix of standard theoretical
                 matrix theory.",
  tableofcontents = "Preface / v \\
                 Summary of Notation / 1 \\
                 1. Basic Concepts of the Theory of Matrices / 5 \\
                 Matrices / 5 \\
                 Determinants / 10 \\
                 Nonsingular matrices. Inverse matrices / 15 \\
                 Schur complement. Factorization / 19 \\
                 Vector spaces. Rank / 24 \\
                 Eigenvectors, eigenvalues. Characteristic polynomial /
                 26 \\
                 Similarity. Jordan normal form / 28 \\
                 Exercises / 36 \\
                 2. Symmetric Matrices. Positive Definite and
                 Semidefinite Matrices / 39 \\
                 Euclidean and unitary spaces / 39 \\
                 Symmetric and Hermitian matrices / 41 \\
                 Orthogonal and unitary matrices / 43 \\
                 Gram--Schmidt orthonormalization. Schur's theorem / 47
                 \\
                 Positive definite and positive semidefinite matrices /
                 51 \\
                 Sylvester's law of inertia / 57 \\
                 Singular value decomposition / 59 \\
                 Exercises / 63 \\
                 3. Graphs and Matrices / 65 \\
                 Digraphs / 65 \\
                 Digraph of a matrix / 70 \\
                 Undirected graphs. Trees / 73 \\
                 Bigraphs / 80 \\
                 Exercises / 85 \\
                 4. Nonnegative Matrices. Stochastic and Doubly
                 Stochastic Matrices / 87 \\
                 Nonnegative matrices / 87 \\
                 The Perron--Frobenius theorem / 90 \\
                 Cyclic matrices / 95 \\
                 Stochastic matrices / 105 \\
                 Doubly stochastic matrices / 107 \\
                 Exercises / 111 \\
                 5. $M$-Matrices (Matrices of Classes $K$ and $K_0$) /
                 112 \\
                 Class $K$ / 114 \\
                 Class $K+0$ / 121 \\
                 Diagonally dominant matrices / 126 \\
                 Monotone matrices / 130 \\
                 Class $P$ / 131 \\
                 Exercises / 135 \\
                 6. Tensor Product of Matrices. Compound Matrices / 136
                 \\
                 Tensor product / 137 \\
                 Compound matrices / 142 \\
                 Exercises / 155 \\
                 7. Matrices and Polynomials. Stable matrices / 157 \\
                 Characteristic polynomial / 157 \\
                 Matrices associated with polynomials / 160 \\
                 B{\'e}zout matrices / 164 \\
                 Hankel matrices / 167 \\
                 Toeplitz and L{\"o}wner matrices / 177 \\
                 Stable matrices / 178 \\
                 Exercises / 186 \\
                 8. Band Matrices / 189 \\
                 Band matrices and graphs / 189 \\
                 Eigenvalues and eigenvectors of tridiagonal matrices /
                 195 \\
                 Exercises / 200 \\
                 9. Norms and Their Use for Estimation of Eigenvalues /
                 201 \\
                 Norms / 201 \\
                 Measure of nonsingularity. Dual norms / 209 \\
                 Bounds for eigenvalues / 215 \\
                 Exercises / 230 \\
                 10. Direct Methods for Solving Linear Systems / 231 \\
                 Nonsingular case / 231 \\
                 General case / 239 \\
                 Exercises / 244 \\
                 11. Iterative Methods for Solving Linear Systems / 245
                 \\
                 The Jacobi method / 247 \\
                 The Gauss--Seidel method / 249 \\
                 The SOR method / 252 \\
                 Exercises / 262 \\
                 12. Matrix Inversion / 264 \\
                 Inversion of special matrices / 264 \\
                 The pseudoinverse / 270 \\
                 Exercises / 271 \\
                 13. Numerical Methods for Computing Eigenvalues of
                 Matrices / 273 \\
                 Computation of selected eigenvalues / 273 \\
                 Computation of all the eigenvalues / 276 \\
                 Exercises / 284 \\
                 14. Sparse matrices / 286 \\
                 Storing. Elimination ordering / 286 \\
                 Envelopes. Profile / 294 \\
                 Exercises / 298 \\
                 Bibliography / 299 \\
                 Subject Index / 303",
}

@Book{Finkbeiner:1960:IML,
  author =       "Daniel T. (Daniel Talbot) {Finkbeiner II}",
  title =        "Introduction to Matrices and Linear Transformations",
  publisher =    pub-W-H-FREEMAN,
  address =      pub-W-H-FREEMAN:adr,
  pages =        "248",
  year =         "1960",
  LCCN =         "QA263 .F45",
  bibdate =      "Sat Nov 22 18:28:44 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "A Series of undergraduate books in mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "1919--",
  remark =       "Drawings by Evan Gillespie.",
  subject =      "Matrices; Algebras, Linear",
}

@Book{Finkbeiner:1966:IML,
  author =       "Daniel T. (Daniel Talbot) {Finkbeiner II}",
  title =        "Introduction to Matrices and Linear Transformations",
  publisher =    pub-W-H-FREEMAN,
  address =      pub-W-H-FREEMAN:adr,
  edition =      "Second",
  pages =        "xi + 297",
  year =         "1966",
  LCCN =         "QA263 .F45 1966",
  bibdate =      "Sat Nov 22 18:28:44 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "A Series of books in mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "1919--",
  subject =      "Matrices; Algebras, Linear",
}

@Book{Finkbeiner:1978:IML,
  author =       "Daniel T. (Daniel Talbot) {Finkbeiner II}",
  title =        "Introduction to Matrices and Linear Transformations",
  publisher =    pub-W-H-FREEMAN,
  address =      pub-W-H-FREEMAN:adr,
  edition =      "Third",
  pages =        "xii + 462",
  year =         "1978",
  ISBN =         "0-7167-0084-0",
  ISBN-13 =      "978-0-7167-0084-5",
  LCCN =         "QA188 .F56 1978",
  bibdate =      "Sat Nov 22 18:28:44 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "A Series of books in the mathematical sciences",
  acknowledgement = ack-nhfb,
  author-dates = "1919--",
  subject =      "Matrices; Algebras, Linear",
}

@Book{Finkbeiner:2011:IML,
  author =       "Daniel T. (Daniel Talbot) {Finkbeiner II}",
  title =        "Introduction to Matrices and Linear Transformations",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Dover",
  pages =        "xii + 462",
  year =         "2011",
  ISBN =         "0-486-48159-X",
  ISBN-13 =      "978-0-486-48159-3",
  LCCN =         "QA188 .F56 2011",
  bibdate =      "Sat Nov 22 18:28:44 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy1106/2010048976-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1318/2010048976-t.html",
  acknowledgement = ack-nhfb,
  author-dates = "1919--",
  remark =       "Originally published: 3rd ed. San Francisco: W.H.
                 Freeman, 1978, in series: A series of books in the
                 mathematical sciences.",
  subject =      "Matrices; Algebras, Linear",
}

@Book{Franklin:1968:MT,
  author =       "Joel N. Franklin",
  title =        "Matrix Theory",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 292",
  year =         "1968",
  LCCN =         "QA263 .F72",
  MRclass =      "15.00 (65.00)",
  MRnumber =     "0237517 (38 \#5798)",
  MRreviewer =   "E. L. Albasiny",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Franklin:2000:MT,
  author =       "Joel N. Franklin",
  title =        "Matrix theory",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xii + 292",
  year =         "2000",
  ISBN =         "0-486-41179-6 (paperback)",
  ISBN-13 =      "978-0-486-41179-8 (paperback)",
  LCCN =         "QA188 .F66 2000",
  bibdate =      "Sun Nov 23 07:58:14 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover031/99058316.html;
                 http://www.loc.gov/catdir/toc/dover031/99058316.html",
  acknowledgement = ack-nhfb,
  remark =       "Originally published in \cite{Franklin:1968:MT}.",
  subject =      "Matrices",
}

@Book{Gantmacher:1959:ATM,
  author =       "F. R. (Feliks Ruvimovich) Gantmacher",
  title =        "Applications of the Theory of Matrices",
  publisher =    "Interscience Publishers, Inc.",
  address =      "New York, NY, USA",
  pages =        "ix + 317",
  year =         "1959",
  LCCN =         "QA263 .G3532",
  MRclass =      "15.00 (65.00)",
  MRnumber =     "0107648 (21 \#6372b)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Translated by J. L. Brenner, with the assistance of D.
                 W. Bushaw and S. Evanusa",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1908--1964",
  remark =       "Translation, with revisions, of the second part of
                 \booktitle{A theory of matrices}. Translated and rev.
                 by J.L. Brenner and with the assistance of D.W. Bushaw
                 and S. Evanusa",
  xxpublisher =  "Interscience Publishers, Inc., New York; Interscience
                 Publishers Ltd., London",
}

@Book{Gantmacher:1959:TMa,
  author =       "F. R. (Feliks Ruvimovich) Gantmacher",
  title =        "The Theory of Matrices",
  volume =       "1",
  publisher =    "Chelsea Publishing Company",
  address =      "New York, NY, USA",
  pages =        "x + 374",
  year =         "1959",
  LCCN =         "QA263.G35 1960 vol. 1",
  bibdate =      "Fri Nov 21 08:39:35 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1908--1964",
}

@Book{Gantmacher:1959:TMb,
  author =       "F. R. (Feliks Ruvimovich) Gantmacher",
  title =        "The Theory of Matrices",
  volume =       "2",
  publisher =    "Chelsea Publishing Company",
  address =      "New York, NY, USA",
  pages =        "ix + 276",
  year =         "1959",
  LCCN =         "QA263.G35 1960 vol. 2",
  bibdate =      "Fri Nov 21 08:39:35 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1908--1964",
  xxauthor =     "F. R. (Feliks Ruvimovich) Gantmacher and K. A.
                 Hirsch",
}

@Book{Gantmacher:1960:OOK,
  author =       "F. R. (Feliks Ruvimovich) Gantmacher and M. G.
                 Kre{\u\i}n",
  title =        "{Oszillationsmatrizen, Oszillationskerne und kleine
                 Schwingungen mechanischer Systeme}. ({German})
                 [Oscillation matrices, oscillation kernels, and small
                 vibrations of mechanical systems]",
  volume =       "5",
  publisher =    pub-AKADEMIE-VERLAG,
  address =      pub-AKADEMIE-VERLAG:adr,
  pages =        "x + 359",
  year =         "1960",
  LCCN =         "QA871 .G315",
  MRclass =      "70.00",
  MRnumber =     "0114338 (22 \#5161)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Wissenschaftliche Bearbeitung der deutschen Ausgabe:
                 Alfred St{\"o}hr. Mathematische Lehrb{\"u}cher und
                 Monographien, I. Abteilung, Bd. V",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  language =     "German",
}

@Book{Gantmakher:2005:ATM,
  author =       "F. R. (Feliks Ruvimovich) Gantmakher",
  title =        "Applications of the Theory of Matrices",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "ix + 317",
  year =         "2005",
  ISBN =         "0-486-44554-2 (paperback)",
  ISBN-13 =      "978-0-486-44554-0 (paperback)",
  LCCN =         "QA263 .G3532 2005",
  bibdate =      "Sun Nov 23 07:59:29 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translated by J. L. Brenner and with the assistance of
                 D. W. Busaw and S. Evanusa.",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0624/2005047409-d.html",
  acknowledgement = ack-nhfb,
  remark =       "Originally published in \cite{Gantmacher:1959:ATM}.",
  subject =      "Matrices",
}

@Book{Glazman:2006:FDL,
  author =       "I. M. Glazman and Ju. I. Ljubi{\v{c}}",
  title =        "Finite-Dimensional Linear Analysis: a Systematic
                 Presentation in Problem Form",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xx + 520",
  year =         "2006",
  ISBN =         "0-486-45332-4",
  ISBN-13 =      "978-0-486-45332-3",
  LCCN =         "QA320 .G5513 2006",
  MRclass =      "46-02 (15-02 47-02)",
  MRnumber =     "2302906 (2007m:46002)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Translated from the Russian \booktitle{Konechnomernyi
                 lineinyi analiz v zadachakh}, and edited by G. P.
                 Barker and G. Kuerti. Reprint of the 1974 MIT Press
                 (Cambridge, MA, USA) edition.",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0643/2006045447-d.html;
                 http://www.zentralblattmath.org/zmath/en/search/?an=1115.46001",
  ZMnumber =     "1115.46001",
  abstract =     "This remarkable book takes a unique approach to linear
                 algebra, presenting a logically interconnected sequence
                 of propositions and problems -- 2,400 in all -- with
                 hints and pointers, but without proofs. Advanced
                 undergraduates and graduate students work out formal
                 proofs systematically, proceeding from simple
                 verifications to advanced strategies and techniques of
                 proof.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Gohberg:1969:ITL,
  author =       "I. C. Gohberg and M. G. Kre{\u\i}n",
  title =        "Introduction to the Theory of Linear Nonselfadjoint
                 Operators",
  volume =       "18",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xv + 378",
  year =         "1969",
  ISBN =         "0-8218-1568-7",
  ISBN-13 =      "978-0-8218-1568-7",
  LCCN =         "QA320 .G6313",
  MRclass =      "47.10",
  MRnumber =     "0246142 (39 \#7447)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Translated from the Russian by A. Feinstein.",
  series =       "Translations of Mathematical Monographs",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Gohberg:1982:MP,
  author =       "I. Gohberg and P. Lancaster and L. Rodman",
  title =        "Matrix Polynomials",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiv + 409",
  year =         "1982",
  ISBN =         "0-12-287160-X",
  ISBN-13 =      "978-0-12-287160-3",
  LCCN =         "QA188 .G64 1982",
  MRclass =      "15A18 (15-02 15A21 15A24 47A56)",
  MRnumber =     "662418 (84c:15012)",
  MRreviewer =   "Heinz Langer",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Computer Science and Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/description/els033/81022792.html;
                 http://www.loc.gov/catdir/toc/els031/81022792.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface \\
                 Introduction \\
                 Linearization and Standard Pairs \\
                 Representation of Monic Matrix Polynomials \\
                 Multiplication and Divisibility \\
                 Spectral Divisors and Canonical Factorization \\
                 Perturbation and Stability of Divisors \\
                 Extension Problems \\
                 Spectral Properties and Representations \\
                 Applications to Differential and Difference Equations
                 \\
                 Least Common Multiples and Greatest Common Divisors of
                 Matrix Polynomials \\
                 General Theory \\
                 Factorization of Self-Adjoint Matrix Polynomials \\
                 Further Analysis of the Sign Characteristic \\
                 Quadratic Self-Adjoint Polynomials \\
                 The Smith Form and Related Problems \\
                 The Matrix Equation $A X - X B = C$ \\
                 One Sided and Generalized Inverses \\
                 Stable Invariant Subspaces \\
                 Indefinite Scalar product Spaces \\
                 Analytic Matrix Functions \\
                 References",
}

@Book{Gohberg:1983:MIS,
  author =       "I. Gohberg and P. Lancaster and L. Rodman",
  title =        "Matrices and Indefinite Scalar Products",
  volume =       "8",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xvii + 374",
  year =         "1983",
  ISBN =         "3-7643-1527-X",
  ISBN-13 =      "978-3-7643-1527-6",
  LCCN =         "QA329.2 .G63 1983",
  MRclass =      "15-01",
  MRnumber =     "859708 (87j:15001)",
  MRreviewer =   "F. Uhlig",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Operator Theory: Advances and Applications",
  URL =          "http://www.gbv.de/dms/ilmenau/toc/024274224.PDF",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Linear operators; Matrices; Indefinite inner product
                 spaces",
  tableofcontents = "Introduction / 1 \\
                 Part I. Basic Theory / 9 \\
                 1. Indefinite Scalar Products \\
                 1.1 Definition / 10 \\
                 1.2 Orthogonality and orthogonal bases / 12 \\
                 1.3 Classification of subspaces / 15 \\
                 2. Classes of Linear Transformations \\
                 2.1 AdJoint matrices / 19 \\
                 2.2 $H$-selfadjoint matrices; examples and simplest
                 properties / 22 \\
                 2.3 $H$-unitary matrices; examples and simplest
                 properties / 25 \\
                 2.4 A second characterization of $H$-unitary matrices /
                 29 \\
                 3. Canonical Forms of $H$-Selfadjoint Matrices \\
                 3.1 Unitary similarity / 31 \\
                 3.2 Description of a canonical form / 33 \\
                 3.3 First applications of the canonical form / 35 \\
                 3.4 Proof of Theorem 3.3 / 37 \\
                 3.5 Classification of matrices by unitary similarity /
                 43 \\
                 3.6 Signature matrices / 47 \\
                 3.7 The structure of $H$-selfadjoint matrices when H
                 has a small number of negative eigenvalues / 52 \\
                 3.8 $H$-definite matrices / 54 \\
                 3.9 Second description of the sign characteristic / 55
                 \\
                 3.10 Canonical forms for pairs of Hermitian matrices /
                 57 \\
                 3.11 Third description of the sign characteristic / 59
                 \\
                 3.12 Maximal nonnegative invariant subspaces / 61 \\
                 3.13 Inverse problems / 68 \\
                 4. Canonical Forms For $H$-Unitary Matrices \\
                 4.1 First examples of canonical forms / 70 \\
                 4.2 Canonical forms in the general case / 73 \\
                 4.3 Correctness of the sign characteristic / 79 \\
                 4.4 First applications of the canonical form / 82 \\
                 4.5 Further deductions from the canonical form / 83 \\
                 4.6 $H$-normal matrices / 84 \\
                 5. Real Matrices \\
                 5.1 Real $H$-selfadjoint matrices and canonical forms /
                 87 \\
                 5.2 Proof of Theorem 5.3 / 91 \\
                 5.3 Comparison with results in the complex case / 95
                 \\
                 5.4 Connected components of real unitary similarity
                 classes / 96 \\
                 5.5 Connected components of real unitary similarity
                 classes (H fixed) / 102 \\
                 6. Functions of $H$-Selfadjoint and $H$-Unitary
                 Matrices \\
                 6.1 Preliminaries / 106 \\
                 6.2 Exponential and logarithmic functions / 108 \\
                 6.3 Functions of $H$-selfadjoint matrices / 110 \\
                 6.4 Functions of $H$-unitary matrices / 114 \\
                 6.5 The canonical form and sign characteristic for a
                 function of an $H$-selfadjoint matrix / 115 \\
                 6.6 Functions of $H$-selfadjoint matrices which are
                 selfadjoint in another indefinite scalar product / 119
                 \\
                 Notes To Part I / 121 \\
                 Part II. First Applications / 123 \\
                 1. Hamiltonian and Selfadjoint Differential Equations
                 with Periodic Coefficients \\
                 1.1 The matrizant / 126 \\
                 1.2 The monodromy matrix / 131 \\
                 1.3 The Floquet theorem / 133 \\
                 1.4 The real case / 134 \\
                 1.5 Proof of Theorem 1.7 / 136 \\
                 1.6 Selfadjoint equations with periodic coefficients /
                 138 \\
                 1.7 The real case for selfadjoint equations 144 \\
                 1.8 Boundedness of solutions of selfadjoint equations /
                 145 \\
                 2. Hermitian Matrix Polynomials \\
                 2.1 Preliminaries 149 \\
                 2.2 Matrix polynomials with Hermitian coefficients /
                 152 \\
                 2.3 Factorization,of Hermitian matrix polynomials / 156
                 \\
                 2.4 Difference equations and Hermitian matrix
                 polynomials on the unit circle / 160 \\
                 3. Hermitian Rational Matrix Functions \\
                 3.1 Minimal nodes / 166 \\
                 3.2 The sign characteristic: definition and main result
                 / 168 \\
                 3.3 Null functions and Jordan chains / 171 \\
                 3.4 Proof of Theorem 3.4 / 174 \\
                 3.5 Factorization of Hermitian rational matrix
                 functions / 177 \\
                 3.6 Symmetric factorizations of Hermitian rational
                 matrix functions / 179 \\
                 3.7 Nonnegative definite rational matrix functions /
                 183 \\
                 3.8 Minimal factorizations of real Hermitian rational
                 matrix functions / 186 \\
                 Appendix to Chapter 3. Rational Matrix Functions \\
                 A.1 Linear Systems, their transfer functions and nodes
                 / 188 \\
                 A.2 The local Smith form and partial multiplicities /
                 193 \\
                 A.3 Minimal factorizations / 195 \\
                 A.4 Minimal factorizations of real rational functions /
                 199 \\
                 4. The Algebraic Riccati Equation \\
                 4.1 An optimal control problem / 202 \\
                 4.2 General Solutions of the Riccati equation / 203 \\
                 4.3 Existence of Hermitian Solutions of the Riccati
                 equation / 208 \\
                 4.4 Hermitian Solutions and nonnegative rational
                 functions / 214 \\
                 4.5 Description of Hermitian Solutions / 217 \\
                 4.6 Extremal Hermitian Solutions / 219 \\
                 4.7 Real Symmetric solutions of the algebraic Riccati
                 equation with real coefficients / 223 \\
                 Notes to Part II / 226 \\
                 Part III. Perturbations and Stability / 227 \\
                 1. General Perturbations. Stability of Diagonable
                 Matrices \\
                 1.1 General perturbations of $H$-selfadjoint matrices /
                 229 \\
                 1.2 Stably diagonable $H$-selfadjoint matrices / 232
                 \\
                 1.3 General perturbations and stably diagonable
                 $H$-unitary matrices / 235 \\
                 1.4 Analytic perturbations and eigenvalues / 236 \\
                 1.5 Analytic perturbations and eigenvectors / 241 \\
                 1.6 The real case / 243 \\
                 1.7 The real skew-symmetric case / 244 \\
                 1.8 Auxiliary results for the real skew-symmetric case
                 / 246 \\
                 1.9 Proof of Theorem 1.10 / 248 \\
                 2. Applications to Differential and Difference
                 Equations \\
                 2.1 Differential equations of first order / 251 \\
                 2.2 Differential equations of higher order / 252 \\
                 2.3 The strongly hyperbolic case / 255 \\
                 2.4 Difference equations / 257 \\
                 2.5 Hamiltonian and selfadjoint equations / 260 \\
                 3. Positive Perturbations \\
                 3.1 Positive perturbations of $H$-selfadjoint matrices
                 / 262 \\
                 3.2 Hamiltonian Systems of positive type with constant
                 coefficients / 265 \\
                 4. Perturbations of Invariant Maximal Neutral Subspaces
                 4.1 Continuity of invariant maximal neutral subspaces /
                 268 \\
                 4.2 Analyticity of invariant maximal neutral subspaces
                 / 270 \\
                 4.3 Extremal Solutions of the algebraic Riccati
                 equation / 273 \\
                 4.4 Application to the optimal control problem / 275
                 \\
                 4.5 Continuity of canonical factorization of
                 nonnegative rational matrix functions / 278 \\
                 5. Perturbations Which Preserve Jordan Structure \\
                 5.1 Stability of the sign characteristic / 282 \\
                 5.2 Stability of unitary similarity / 287 \\
                 5.3 Special cases of unitary similarity / 289 \\
                 5.4 Continuous dependence of the canonical form / 291
                 \\
                 5.5 Analytic dependence of the canonical form / 297 \\
                 5.6 $H$-unitary matrices / 298 \\
                 5.7 Connected components of selfadjoint matrices with
                 like real Jordan structure / 299 \\
                 5.8 The real case / 303 \\
                 Appendix to Part III. Subspaces in Finite Dimensional
                 Complex Space \\
                 A.1 The metric space of subspaces / 306 \\
                 A.2 Continuous families of subspaces / 311 \\
                 A.3 Analytic families of subspaces / 315 \\
                 Notes to Part III / 318 \\
                 Part IV. Connected Components of Differential Equations
                 / 319 \\
                 1. Connected Components of Stably Diagonable Matrices
                 \\
                 1.1 $H$-selfadjoint stably $r$-diagonable matrices /
                 320 \\
                 1.2 $H$-unitary stably $u$-diagonable matrices / 323
                 \\
                 1.3 $E$-orthogonal stably $u$-diagonable matrices / 326
                 \\
                 2. Differential And Difference Equations with Constant
                 Coefficients \\
                 2.1 Connected components of differential equations with
                 Hermitian coefficients and stably bounded Solutions /
                 329 \\
                 2.2 A special case / 331 \\
                 2.3 Connected components of difference equations 334
                 \\
                 3. Connected Components of Hamiltonian Equations \\
                 3.1 Definition and explanation of the problem / 338 \\
                 3.2 Group of $H$-unitary matrices / 340 \\
                 3.3 Simple connectedness of unitary similarity classes
                 / 343 \\
                 3.4 Homotopy in connected components of $u$-stably
                 diagonable [sic] matrices / 347 \\
                 3.5 Homotopy indices of $H$-unitary matrices / 350 \\
                 3.6 Connected components of Hamiltonian Systems with
                 stably bounded Solutions / 354 \\
                 3.7 Simple connectedness of connected components of
                 real $E$-orthogonal matrices / 356 \\
                 3.8 Connected components of real Hamiltonian Systems
                 with stably bounded Solutions / 360 \\
                 Notes to Part IV / 362 \\
                 References / 363 \\
                 List of Notations / 368 \\
                 Index / 370",
}

@Book{Gohberg:2006:ISM,
  author =       "Israel Gohberg and Peter Lancaster and Leiba Rodman",
  title =        "Invariant Subspaces of Matrices with Applications",
  volume =       "51",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxi + 692",
  year =         "2006",
  DOI =          "https://doi.org/10.1137/1.9780898719093",
  ISBN =         "0-89871-608-X",
  ISBN-13 =      "978-0-89871-608-5",
  LCCN =         "QA322 .G649 2006",
  MRclass =      "15-01 (15-02 47A15)",
  MRnumber =     "2228089 (2007k:15001)",
  MRreviewer =   "Edward Azoff",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Reprint of the 1986 original.",
  series =       "Classics in Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0665/2006042260-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0665/2006042260-t.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "Israel Gohberg (1928--)",
  remark =       "Originally published: New York: Wiley, 1986, in
                 series: Canadian Mathematical Society series of
                 monographs and advanced texts.",
  tableofcontents = "Preface to the classics edition \\
                 Preface to the first edition \\
                 Introduction \\
                 Part I. Fundamental Properties of Invariant Subspaces
                 and Applications \\
                 1. Invariant subspaces \\
                 2. Jordan form and invariant subspaces \\
                 3. Coinvariant and semiinvariant subspaces \\
                 4. Jordan form for extensions and completions \\
                 5. Applications to matrix polynomials \\
                 6. Invariant subspaces for transformations between
                 different spaces \\
                 7. Rational matrix functions \\
                 8. Linear systems \\
                 Part II. Algebraic Properties of Invariant Subspaces
                 \\
                 9. Commuting matrices and hyperinvariant subspaces \\
                 10. Description of invariant subspaces and linear
                 transformation with the same invariant subspaces \\
                 11. Algebras of matrices and invariant subspaces \\
                 12. Real linear transformations \\
                 Part III. Topological Properties of Invariant Subspaces
                 and Stability \\
                 13. The metric space of subspaces \\
                 14. The metric space of invariant subspaces \\
                 15. Continuity and stability of invariant subspaces \\
                 16. Perturbations of lattices of invariant subspaces
                 with restrictions on the Jordan structure \\
                 17. Applications \\
                 Part IV. Analytic Properties of Invariant Subspaces \\
                 18. Analytic families of subspaces \\
                 19. Jordan form of analytic matrix functions \\
                 20. Applications \\
                 Appendix \\
                 References \\
                 Author index \\
                 Subject index",
}

@Book{Golan:2004:LAB,
  author =       "Jonathan S. Golan",
  title =        "The Linear Algebra a Beginning Graduate Student Ought
                 to Know",
  volume =       "27",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "x + 406",
  year =         "2004",
  ISBN =         "1-4020-1824-X (hardcover)",
  ISBN-13 =      "978-1-4020-1824-4 (hardcover)",
  LCCN =         "QA184.2 .G65 2004",
  MRclass =      "15-01 (00-01); 15-01, 15A03, 15A04, 15A06, 15A09,
                 15A15, 15A18, 15A63",
  MRnumber =     "2140296 (2006c:15001)",
  MRreviewer =   "David Scott Watkins",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Kluwer Texts in the Mathematical Sciences",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Notation and terminology \\
                 Fields \\
                 Vector spaces over a field \\
                 Algebras over a field \\
                 Linear dependence and dimension \\
                 Linear transformations \\
                 The endomorphism algebra of a vector space \\
                 Representation of linear transformations by matrices
                 \\
                 The algebra of square matrices \\
                 Systems of linear equations \\
                 Determinants \\
                 Eigenvalues and Eigenvectors \\
                 Krylov subspaces \\
                 The dual space \\
                 Inner product spaces \\
                 Orthogonality \\
                 Selfadjoint endomorphisms \\
                 Unitary and normal endomorphisms \\
                 Moore--Penrose pseudoinverses \\
                 Bilinear transformations and forms \\
                 Appendix A. Summary of notation",
}

@Book{Golub:1996:MC,
  author =       "Gene H. Golub and Charles F. {Van Loan}",
  title =        "Matrix Computations",
  publisher =    pub-JOHNS-HOPKINS,
  address =      pub-JOHNS-HOPKINS:adr,
  edition =      "Third",
  pages =        "xxvii + 694",
  year =         "1996",
  ISBN =         "0-8018-5413-X (hardcover), 0-8018-5414-8 (paperback)",
  ISBN-13 =      "978-0-8018-5413-2 (hardcover), 978-0-8018-5414-9
                 (paperback)",
  LCCN =         "QA188 .G65 1996",
  MRclass =      "65-02 (65Fxx)",
  MRnumber =     "1417720 (97g:65006)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  series =       "Johns Hopkins Studies in the Mathematical Sciences",
  URL =          "http://www.loc.gov/catdir/bios/jhu052/96014291.html;
                 http://www.loc.gov/catdir/description/jhu051/96014291.html",
  acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah # "
                 and " # ack-crj,
  author-dates = "Gene H. Golub (1932--2007)",
  tableofcontents = "Preface to the Third Edition / xi \\
                 Software / xiii \\
                 Selected References / xv \\
                 1: Matrix Multiplication Problems \\
                 1.1 Basic Algorithms and Notation / 2 \\
                 1.2 Exploiting Structure / 16 \\
                 1.3 Block Matrices and Algorithms / 24 \\
                 1.4 Vectorization and Re-Use Issues / 34 \\
                 2: Matrix Analysis 48 V 2.1 Basic Ideas from Linear
                 Algebra / 48 \\
                 2.2 Vector Norms / 52 \\
                 2.3 Matrix Norms / 54 \\
                 2.4 Finite Precision Matrix Computations / 59 \\
                 2.5 Orthogonality and the SVD / 69 \\
                 2.6 Projections and the $CS$ Decomposition / 75 \\
                 2.7 The Sensitivity of Square Linear Systems / 80 \\
                 3: General Linear Systems / 87 \\
                 3.1 Triangular Systems / 88 \\
                 3.2 The $L U$ Factorization / 94 \\
                 3.3 Roundoff Analysis of Gaussian Elimination / 104 \\
                 3.4 Pivoting / 109 \\
                 3.5 Improving and Estimating Accuracy / 123 \\
                 4: Special Linear Systems / 133 \\
                 4.1 The $L D M^T$ and $L D L^T$ Factorizations / 135
                 \\
                 4.2 Positive Definite Systems / 140 \\
                 4.3 Banded Systems / 152 \\
                 4.4 Symmetric Indefinite Systems / 161 \\
                 4.5 Block Systems / 174 \\
                 4.6 Vandermonde Systems and the FFT / 183 \\
                 4.7 Toeplitz and Related Systems / 193 \\
                 5: Orthogonalization and Least Squares / 206 \\
                 5.1 Householder and Givens Matrices / 208 \\
                 5.2 The $Q R$ Factorization / 223 \\
                 5.3 The Full Rank LS Problem / 236 \\
                 5.4 Other Orthogonal Factorizations / 248 \\
                 5.5 The Rank Deficient LS Problem / 256 \\
                 5.6 Weighting and Iterative Improvement / 264 \\
                 5.7 Square and Underdetermined Systems / 270 \\
                 6: Parallel Matrix Computations / 275 \\
                 6.1 Basic Concepts / 276 \\
                 6.2 Matrix Multiplication / 292 \\
                 6.3 Factorizations / 300 \\
                 7: The Unsymmetric Eigenvalue Problem / 308 \\
                 7.1 Properties and Decompositions / 310 \\
                 7.2 Perturbation Theory / 320 \\
                 7.3 Power Iterations / 330 \\
                 7.4 The Hessenberg and Real Schur Forms / 341 \\
                 7.5 The Practical $Q R$ Algorithm / 352 \\
                 7.6 Invariant Subspace Computations / 362 \\
                 7.7 The $Q Z$ Method for $A x = \lambda B x$ / 375 \\
                 8: The Symmetric Eigenvalue Problem / 391 \\
                 8.1 Properties and Decompositions / 393 \\
                 8.2 Power Iterations / 405 \\
                 8.3 The Symmetric $Q R$ Algorithm / 414 \\
                 8.4 Jacobi Methods / 426 \\
                 8.5 Tridiagonal Methods / 439 \\
                 8.6 Computing the SVD / 448 \\
                 8.7 Some Generalized Eigenvalue Problems / 461 \\
                 9: Lanczos Methods / 470 \\
                 9.1 Derivation and Convergence Properties / 471 \\
                 9.2 Practical Lanczos Procedures / 479 \\
                 9.3 Applications to $A x = b$ and Least Squares / 490
                 \\
                 9.4 Arnoldi and Unsymmetric Lanczos / 499 \\
                 10: Iterative Methods for Linear Systems / 508 \\
                 10.1 The Standard Iterations / 509 \\
                 10.2 The Conjugate Gradient Method / 520 \\
                 10.3 Preconditioned Conjugate Gradients / 532 \\
                 10.4 Other Krylov Subspace Methods / 544 \\
                 11: Functions of Matrices / 555 \\
                 11.1 Eigenvalue Methods / 556 \\
                 11.2 Approximation Methods / 562 \\
                 11.3 The Matrix Exponential / 572 \\
                 12: Special Topics / 579 \\
                 12.1 Constrained Least Squares / 580 \\
                 12.2 Subset Selection Using the SVD / 590 \\
                 12.3 Total Least Squares / 595 \\
                 12.4 Computing Subspaces with the SVD / 601 \\
                 12.5 Updating Matrix Factorizations / 606 \\
                 12.6 Modified/Structured Eigenproblems / 621 \\
                 Bibliography / 637 \\
                 Index / 687",
}

@Book{Graham:1981:KPM,
  author =       "Alexander Graham",
  title =        "{Kronecker} Products and Matrix Calculus: with
                 Applications",
  publisher =    pub-ELLIS-HORWOOD,
  address =      pub-ELLIS-HORWOOD:adr,
  pages =        "130",
  year =         "1981",
  ISBN =         "0-85312-391-8 (library), 0-85312-427-2 (student),
                 0-470-27300-3 (Halsted Press)",
  ISBN-13 =      "978-0-85312-391-0 (library), 978-0-85312-427-6
                 (student), 978-0-470-27300-5 (Halsted Press)",
  LCCN =         "QA188 .G698 1981",
  MRclass =      "15-02 (15A24 15A69)",
  MRnumber =     "640865 (83g:15001)",
  MRreviewer =   "S. Kurepa",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Ellis Horwood Series in Mathematics and its
                 Applications",
  abstract =     "This book introduces the concept of the Kronecker
                 matrix product and its applications to mathematics,
                 science and engineering. It covers important
                 developments in matrix calculus; and the various
                 techniques which it introduces, which heretofore have
                 been the sole preserve of the expert, are now
                 re-expressed in a manner which is readily
                 understandable, and which is applicable to a wide range
                 of scientific disciplines. We know no of no other text
                 dealing with these topics, at this level.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Kronecker products; Matrices; Kronecker, Produits de;
                 Matrices; Kronecker-structuur; Kronecker-Produkt;
                 Matrix (Mathematik); Matrizenrechnung; Matrices;
                 Kronecker products; Matrices",
  tableofcontents = "Preliminaries \\
                 The Kronecker product \\
                 Some applications for the Kronecker product \\
                 Introduction to matrix calculus \\
                 Further development of matrix calculus including an
                 application of Kronecker products \\
                 The derivative of a matrix with respect to a matrix \\
                 Some applications of matrix calculus",
}

@Book{Graybill:1969:IMA,
  author =       "Franklin A. (Franklin Arno) Graybill",
  title =        "Introduction to Matrices with Applications in
                 Statistics",
  publisher =    "Wadsworth International Group",
  address =      "Belmont, CA, USA",
  pages =        "372",
  year =         "1969",
  LCCN =         "QA263 .G67",
  bibdate =      "Fri Nov 21 08:50:47 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  remark =       "Revised edition published as
                 \cite{Graybill:1983:MAS}.",
  subject =      "Matrices; Linear models (Statistics)",
}

@Book{Graybill:1983:MAS,
  author =       "Franklin A. (Franklin Arno) Graybill",
  title =        "Matrices with Applications in Statistics",
  publisher =    "Wadsworth International Group",
  address =      "Belmont, CA, USA",
  edition =      "Second",
  pages =        "xi + 461",
  year =         "1983",
  ISBN =         "0-534-98038-4",
  ISBN-13 =      "978-0-534-98038-2",
  LCCN =         "QA188 .G715 1983",
  bibdate =      "Fri Nov 21 08:49:42 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wadsworth statistics/probability series",
  acknowledgement = ack-nhfb,
  remark =       "Revised edition of \cite{Graybill:1969:IMA}.",
  subject =      "Matrices; Linear models (Statistics); Modelos lineales
                 (Estad{\'i}stica); Mod{\`e}les lin{\'e}aires
                 (Statistique); Matrices.; Lineaire modellen.; Lineares
                 Modell.; Matrizenrechnung.; Statistik.; Linear models
                 (Statistics); Matrices.",
}

@Book{Greub:1967:MA,
  author =       "Werner Hildbert Greub",
  title =        "Multilinear Algebra",
  volume =       "136",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 224",
  year =         "1967",
  LCCN =         "QA251 .G72",
  MRclass =      "15.00",
  MRnumber =     "0224623 (37 \#222)",
  MRreviewer =   "H. Gross",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Die Grundlehren der Mathematischen Wissenschaften",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1925--",
  xxpages =      "x + 225",
}

@Book{Greub:1978:MA,
  author =       "Werner Hildbert Greub",
  title =        "Multilinear Algebra",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "vii + 294",
  year =         "1978",
  ISBN =         "0-387-90284-8",
  ISBN-13 =      "978-0-387-90284-5",
  LCCN =         "QA184 .G74 1978",
  bibdate =      "Sun Nov 23 08:07:37 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Universitext",
  acknowledgement = ack-nhfb,
  author-dates = "1925--",
  subject =      "Multilinear algebra",
}

@Book{Halmos:1942:FDV,
  author =       "Paul R. (Paul Richard) Halmos",
  title =        "Finite-Dimensional Vector Spaces",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "v + 196",
  year =         "1942",
  LCCN =         "QA601 .H23 1942",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "The University Series in Undergraduate Mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "1916-2006",
}

@Book{Halmos:1958:FDV,
  author =       "Paul R. (Paul Richard) Halmos",
  title =        "Finite-Dimensional Vector Spaces",
  publisher =    "D. Van Nostrand Co., Inc.",
  address =      "Princeton / Toronto / New York / London",
  edition =      "Second",
  pages =        "viii + 200",
  year =         "1958",
  LCCN =         "QA261 .H33 1958",
  MRclass =      "15.0X",
  MRnumber =     "0089819 (19,725b)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "The University Series in Undergraduate Mathematics",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1916-2006",
}

@Book{Halmos:1967:HSP,
  author =       "Paul R. (Paul Richard) Halmos",
  title =        "A {Hilbert} Space Problem Book",
  publisher =    "D. Van Nostrand Co., Inc.",
  address =      "Princeton / Toronto / New York / London",
  pages =        "xvii + 365",
  year =         "1967",
  LCCN =         "QA322 .H3",
  MRclass =      "47.00 (46.00)",
  MRnumber =     "0208368 (34 \#8178)",
  MRreviewer =   "C. R. Putnam",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1916-2006",
}

@Book{Halmos:1982:HSP,
  author =       "Paul R. (Paul Richard) Halmos",
  title =        "A {Hilbert} Space Problem Booko",
  volume =       "19",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xvii + 369",
  year =         "1982",
  ISBN =         "0-387-90685-1",
  ISBN-13 =      "978-0-387-90685-0",
  LCCN =         "QA322.4 .H34 1982",
  bibdate =      "Sun Nov 23 08:13:19 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Graduate texts in mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0905/82000763-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0905/82000763-t.html",
  acknowledgement = ack-nhfb,
  author-dates = "1916--2006",
  subject =      "Hilbert space; Problems, exercises, etc",
}

@Book{Hardy:1934:I,
  author =       "Godfrey H. Hardy and John Edensor Littlewood and
                 George P{\'o}lya",
  title =        "Inequalities",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xii + 314",
  year =         "1934",
  LCCN =         "QA303 .H25",
  bibdate =      "Fri Nov 21 08:53:39 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Godfrey H. Hardy (1877--1947); John Edensor Littlewood
                 1885--1977; George P{\'o}lya 1887--1985",
}

@Book{Hardy:1959:I,
  author =       "Godfrey H. Hardy and John Edensor Littlewood and
                 George P{\'o}lya",
  title =        "Inequalities",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "xii + 324",
  year =         "1959",
  LCCN =         "QA303 .H25",
  bibdate =      "Fri Nov 21 08:53:39 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "Godfrey H. Hardy (1877--1947); John Edensor Littlewood
                 1885--1977; George P{\'o}lya 1887--1985",
}

@Book{Higham:2008:FMT,
  author =       "Nicholas J. Higham",
  title =        "Functions of Matrices: Theory and Computation",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xx + 425",
  year =         "2008",
  DOI =          "https://doi.org/10.1137/1.9780898717778",
  ISBN =         "0-89871-646-2 (paperback)",
  ISBN-13 =      "978-0-89871-646-7 (paperback)",
  LCCN =         "QA188 .H53 2008",
  MRclass =      "15-02 (93B40 93C05)",
  MRnumber =     "2396439 (2009b:15001)",
  MRreviewer =   "Daniel Kressner",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
  note =         "Theory and computation",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0834/2007061811-b.html;
                 http://www.loc.gov/catdir/enhancements/fy0834/2007061811-d.html",
  abstract =     "A thorough and elegant treatment of the theory of
                 matrix functions and numerical methods for computing
                 them, including an overview of applications, new and
                 unpublished research results, and improved algorithms.
                 Key features include a detailed treatment of the matrix
                 sign function and matrix roots; a development of the
                 theory of conditioning and properties of the Frechet
                 derivative; Schur decomposition; block Parlett
                 recurrence; a thorough analysis of the accuracy,
                 stability, and computational cost of numerical methods;
                 general results on convergence and stability of matrix
                 iterations; and a chapter devoted to the $ f(A) b $
                 problem. Ideal for advanced courses and for self-study,
                 its broad content, references and appendix also make
                 this book a convenient general reference. Contains an
                 extensive collection of problems with solutions and
                 MATLAB implementations of key algorithms.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1961--",
  tableofcontents = "1. Theory of matrix functions \\
                 2. Applications \\
                 3. Conditioning \\
                 4. Techniques for general functions \\
                 5. Matrix sign function \\
                 6. Matrix square root \\
                 7. Matrix $p$th root \\
                 8. The polar decomposition \\
                 9. Schur--Parlett algorithm \\
                 10. Matrix exponential \\
                 11. Matrix logarithm \\
                 12. Matrix cosine and sine \\
                 13. Function of matrix times vector: $f(A) b$ \\
                 14. Miscellany",
}

@Book{Hirsch:1974:DED,
  author =       "Morris W. Hirsch and Stephen Smale",
  title =        "Differential Equations, Dynamical Systems, and Linear
                 Algebra",
  volume =       "60",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xi + 358",
  year =         "1974",
  ISBN =         "0-12-349550-4",
  ISBN-13 =      "978-0-12-349550-1",
  LCCN =         "QA3 .P8 vol. 60 QA372",
  MRclass =      "34CXX (15-XX 58FXX 70.34)",
  MRnumber =     "0486784 (58 \#6484)",
  MRreviewer =   "Carl P. Simon",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Pure and Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/description/els031/73018951.html;
                 http://www.loc.gov/catdir/toc/els031/73018951.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface \\
                 First Examples \\
                 Newton's Equation and Kepler's Law \\
                 Linear Systems with Constant Coefficients and Real
                 Eigenvalues \\
                 Linear Systems with Constant Coefficients and Complex
                 Eigenvalues \\
                 Linear Systems and Exponentials of Operators \\
                 Linear Systems and Canonical Forms of Operators \\
                 Contractions and Generic Properties of Operators \\
                 Fundamental Theory \\
                 Stability of Equilibria \\
                 Differential Equations for Electrical Circuits \\
                 The Poincar{\'e}--Bendixson Theorem \\
                 Ecology \\
                 Periodic Attractors \\
                 Classical Mechanics \\
                 Nonautonomous Equations and Differentiability of Flows
                 \\
                 Perturbation Theory and Structural Stability \\
                 Elementary Facts \\
                 Polynomials \\
                 On Canonical Forms \\
                 The Inverse Function Theorem \\
                 References \\
                 Answers to Selected Problems \\
                 Index",
}

@Book{Hoffman:1961:LA,
  author =       "Kenneth Hoffman and Ray Alden Kunze",
  title =        "Linear Algebra",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "332",
  year =         "1961",
  LCCN =         "QA251 .H67 1961",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
}

@Book{Hoffman:1971:LA,
  author =       "Kenneth Hoffman and Ray Alden Kunze",
  title =        "Linear Algebra",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  edition =      "Second",
  pages =        "viii + 407",
  year =         "1971",
  ISBN =         "0-13-536797-2",
  ISBN-13 =      "978-0-13-536797-1",
  LCCN =         "QA251 .H67 1971",
  MRclass =      "15.00",
  MRnumber =     "0276251 (43 \#1998)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Algebras, Linear",
}

@Book{Hogben:2007:HLA,
  editor =       "Leslie Hogben",
  booktitle =    "Handbook of Linear Algebra",
  title =        "Handbook of Linear Algebra",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xxx + 1370",
  year =         "2007",
  ISBN =         "1-58488-510-6 (hardcover), 1-4200-1057-3 (e-book)",
  ISBN-13 =      "978-1-58488-510-8 (hardcover), 978-1-4200-1057-2
                 (e-book)",
  LCCN =         "QA184.2 .H36 2007",
  MRclass =      "15-00 (00A20)",
  MRnumber =     "2279160 (2007j:15001)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Associate editors: Richard Brualdi, Anne Greenbaum and
                 Roy Mathias.",
  series =       "Discrete Mathematics and its Applications (Boca
                 Raton)",
  URL =          "http://www.crcnetbase.com/isbn/9781420010572;
                 http://www.crcnetbase.com/isbn/9781584885108;
                 http://www.loc.gov/catdir/enhancements/fy0647/2006045491-d.html",
  abstract =     "\booktitle{Handbook of Linear Algebra} covers all
                 aspects of linear algebra, including fundamentals,
                 numerical linear algebra, software packages for
                 computation in linear algebra, and various
                 applications, such as quantum computing, control
                 theory, image compression, and computational biology.
                 The author addresses combinatorial Matrix theory and
                 features Matrix notation throughout the text. The book
                 includes a chapter on software that provides extensive
                 coverage of MATLAB, Maple, and Mathematica and contains
                 details of Fortran subroutines available for linear
                 algebra such as LAPACK and ARPACK. Rather than
                 presenting long mathematical proofs, the text provides
                 numerous references for additional information.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  keywords =     "Maple",
  remark =       "Associate editors: Richard Brualdi, Anne Greenbaum,
                 and Roy Mathias.",
  subject =      "Algebras, Linear",
  tableofcontents = "Preliminaries \\
                 I. Linear algebra \\
                 1: Vectors, matrices and systems of linear equations /
                 Jane Day \\
                 2: Linear independence, span, and bases / Mark Mills
                 \\
                 3: Linear transformations / Francesco Barioli \\
                 4: Determinants and eigenvalues / Luz M. DeAlba \\
                 5: Inner product spaces, orthogonal projection, least
                 squares and singular value decomposition / Lixing Han
                 and Michael Neumann \\
                 6: Canonical forms / Leslie Hogben \\
                 7: Unitary similarity, normal matrices, and spectral
                 theory / Helene Shapiro \\
                 8: Hermitian and positive definite matrices / Wayne
                 Barrett \\
                 9: Nonnegative and stochastic matrices / Uriel G.
                 Rothblum \\
                 10: Partitioned matrices / Robert Reams \\
                 11: Functions of matrices / Nicholas J. Higham \\
                 12: Quadratic, bilinear and sesquilinear forms /
                 Raphael Lowey \\
                 13: Multilinear algebra / J. A. Dias de Silva and
                 Armando Machado \\
                 14: Matrix equalities and inequalities / Michael
                 Tsatsomeros \\
                 15: Matrix perturbation theory / Ren-Cang Li \\
                 16: Pseudospectra / Mark Embree \\
                 17: Singular values and singular value inequalities /
                 Roy Mathias \\
                 18: Numerical range / Chi-Kwong Li \\
                 19: Matrix stability and inertia / Daniel Hershkowitz
                 \\
                 20: Inverse eigenvalue problems / Alberto Borobia \\
                 21: Totally positive and totally negative matrices /
                 Shaun M. Fallat \\
                 22: Linear preserver problems / Peter \v Semrl \\
                 23: Matrices over integral domains / Shmuel Friedland
                 \\
                 24: Similarities of families of matrices / Shmuel
                 Friedland \\
                 25: Max-plus algebra / Marianne Akian, Ravindra Bapat,
                 St{\'e}phane Gaubert \\
                 26: Matrices leaving a cone invariant / Bit-Shun Tam
                 and Hans Schneider \\
                 II. Combinatorial matrix theory and graphs \\
                 27: Combinatorial matrix theory / Richard A. Brualdi
                 \\
                 28: Matrices and graphs / Willem H. Haemers \\
                 29: Digraphs and matrices / Jeffrey L. Stuart \\
                 30: Bipartite graphs and matrices / Bryan L. Shader \\
                 31: Permanents / Ian M. Wanless \\
                 32: D-optimal designs / Michael G. Neubauer and William
                 Watkins \\
                 33: Sign pattern matrices / Frank J. Hall and Zhongshan
                 Li \\
                 34: Multiplicity lists for the eigenvalues of symmetric
                 matrices with a given graph / Charles R. Johnson,
                 Ant{\'o}nio Leal Duarte, and Carlos M. Saiago \\
                 35: Matrix completion problems / Leslie Hogben and Amy
                 Wangsness \\
                 36: Algebraic connectivity / Steve Kirkland \\
                 III. Numerical methods \\
                 37: Vector and matrix norms, error analysis, efficiency
                 and stability / Ralph Byers and Biswa Nath Datta \\
                 38: Matrix factorizations, and direct solution of
                 linear systems / Christopher Beattie \\
                 39: Least squares solution of linear systems / Per
                 Christian Hansen and Hans Bruun Nielsen \\
                 40: Sparse matrix methods / Esmond G. Ng \\
                 41: Iterative solution methods for linear systems /
                 Anne Greenbaum \\
                 42: Symmetric matrix eigenvalue techniques / Ivan
                 Slapni{\v{c}}ar \\
                 43: Unsymmetric matrix eigenvalue techniques / David S.
                 Watkins \\
                 44: The implicitly restarted Arnoldi method / D. C.
                 Sorensen \\
                 45: Computation of the singular value decomposition /
                 Alan Kaylor Cline and Inderjit S. Dhillon \\
                 46: Computing eigenvalues and singular values to high
                 relative accuracy / Zlatko Drma{\v{c}} \\
                 47: Fast matrix multiplication / Dario A. Bini \\
                 48: Structured matrix computations / Michael Ng \\
                 49: Large-scale matrix computations / Roland W. Freund
                 \\
                 IV. Applications \\
                 50: Linear programming / Leonid S. Vaserstein \\
                 51: Semidefinite programming / Henry Wolkowicz \\
                 52: Random vectors and linear statistical models / Simo
                 Puntanen and George P. H. Styan \\
                 53: Multivariate statistical analysis / Simo Puntanen,
                 George A. F. Seber, and George P. H. Styan \\
                 54: Markov chains / Beatrice Meini \\
                 55: Differential equations and stability / Volker
                 Mehrmann and Tatjana Stykel \\
                 56: Dynamical systems and linear algebra / Fritz
                 Colonius and Wolfgang Kliemann \\
                 57: Control theory / Peter Benner \\
                 58: Fourier analysis / Kenneth Howell \\
                 59: Linear algebra and mathematical physics / Lorenzo
                 Sadun \\
                 60: Linear algebra in biomolecular modeling / Zhijun Wu
                 \\
                 61: Coding theory / Joachim Rosenthal and Paul Weiner
                 \\
                 62: Quantum computation / Zijian Diao \\
                 63: Information retrieval and web search / Amy
                 Langville and Carl Meyer \\
                 64: Signal processing / Michael Stewart \\
                 65: Geometry / Mark Hunacek \\
                 66: Some applications of matrices and graphs in
                 Euclidean geometry / Miroslav Fiedler \\
                 67: Matrix groups / Peter J. Cameron \\
                 68: Group representations / Randall Holmes and T. Y.
                 Tam \\
                 69: Nonassociative algebras / Murray R. Bremner, Lucia
                 I. Muakami and Ivan P. Shestakov \\
                 70: Lie algebras / Robert Wilson \\
                 V. Computational software \\
                 71: MATLAB / Steven J. Leon \\
                 72: Linear algebra in Maple / David J. Jeffrey and
                 Robert M. Corless \\
                 73: Mathematica / Heikki Ruskeep{\"a}{\"a} \\
                 74: BLAS / Jack Dongarra, Victor Eijkhout, and Julien
                 Langou \\
                 75: LAPACK / Zhaojun Bai \\
                 76: Use of ARPACK and EIGS / D. C. Sorensen \\
                 77: Summary of Software for Linear Algebra Freely
                 Available on the Web / Jack Dongarra, Victor Eijkhout,
                 Julien Langou \\
                 G-1: Glossary \\
                 H-1: Notation Index",
}

@Book{Horn:1991:TMA,
  author =       "Roger A. Horn and Charles R. Johnson",
  title =        "Topics in Matrix Analysis",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "viii + 607",
  year =         "1991",
  DOI =          "https://doi.org/10.1017/CBO9780511840371",
  ISBN =         "0-521-30587-X",
  ISBN-13 =      "978-0-521-30587-7",
  LCCN =         "QA188 .H664 1991",
  MRclass =      "15-02 (15-01 65-02)",
  MRnumber =     "1091716 (92e:15003)",
  MRreviewer =   "S. Lajos",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
  URL =          "http://www.loc.gov/catdir/description/cam023/86023310.html;
                 http://www.loc.gov/catdir/toc/cam023/86023310.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "1. The field of values \\
                 2. Stable matrices and inertia \\
                 3. Singular value inequalities \\
                 4. Matrix equations and Kronecker products \\
                 5. Hadamard products \\
                 6. Matrices and functions \\
                 7. Totally positive matrices",
}

@Book{Horn:1985:MA,
  author =       "Roger A. Horn and Charles R. Johnson",
  title =        "Matrix Analysis",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xiii + 561",
  year =         "1985",
  DOI =          "https://doi.org/10.1017/CBO9780511810817",
  ISBN =         "0-521-30586-1 (hardcover), 0-521-38632-2 (paperback),
                 0-511-81081-4 (e-book)",
  ISBN-13 =      "978-0-521-30586-0 (hardcover), 978-0-521-38632-6
                 (paperback), 978-0-511-81081-7 (e-book)",
  LCCN =         "QA188 .H66 1985",
  bibdate =      "Mon Nov 24 09:50:11 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.gbv.de/dms/bowker/toc/9780521305860.pdf;
                 http://www.gbv.de/dms/hbz/toc/ht002524989.pdf;
                 http://www.gbv.de/dms/ilmenau/toc/196021510.PDF;
                 http://www.gbv.de/dms/ilmenau/toc/576799351.PDF;
                 http://www.loc.gov/catdir/description/cam023/85007736.html;
                 http://www.loc.gov/catdir/toc/cam023/85007736.html;
                 http://www.zentralblattmath.org/zmath/en/search/?an=0704.15002",
  ZMnumber =     "0704.15002",
  abstract =     "Linear algebra and matrix theory have long been
                 fundamental tools in mathematical disciplines as well
                 as fertile fields for research. In this book the
                 authors present classical and recent results of matrix
                 analysis that have proved to be important to applied
                 mathematics. Facts about matrices, beyond those found
                 in an elementary linear algebra course, are needed to
                 understand virtually any area of mathematical science,
                 but the necessary material has appeared only
                 sporadically in the literature and in university
                 curricula. As interest in applied mathematics has
                 grown, the need for a text and reference offering a
                 broad selection of topics in matrix theory has become
                 apparent, and this book meets that need. This volume
                 reflects two concurrent views of matrix analysis.
                 First, it encompasses topics in linear algebra that
                 have arisen out of the needs of mathematical analysis.
                 Second, it is an approach to real and complex linear
                 algebraic problems that does not hesitate to use
                 notions from analysis.",
  acknowledgement = ack-nhfb,
  remark =       "Reissued in at least 23 printings (1985--2010).",
  subject =      "Matrices; forme canonique; matrice hermitienne;
                 matrice positive; matrice sym{\'e}trique; matrice non
                 n{\'e}gative; analyse matricielle; valeur propre;
                 matrice; Alg{\`e}bre; Matrices; Alg{\`e}bre
                 lin{\'e}aire; Matrices",
  tableofcontents = "Preface / ix \\
                 Chapter 0 Review and miscellanea / 1 \\
                 0.0 Introduction / 1 \\
                 0.1 Vector spaces / 1 \\
                 0.2 Matrices / 4 \\
                 0.3 Determinants / 7 \\
                 0.4 Rank / 12 \\
                 0.5 Nonsingularity / 14 \\
                 0.6 The usual inner product / 14 \\
                 0.7 Partitioned matrices / 17 \\
                 0.8 Determinants again / 19 \\
                 0.9 Special types of matrices / 23 \\
                 0.10 Change of basis / 30 \\
                 Chapter 1 Eigenvalues, eigenvectors, and similarity /
                 33 \\
                 1.0 Introduction / 33 \\
                 1.1 The eigenvalue-eigenvector equation / 34 \\
                 1.2 The characteristic polynomial / 38 \\
                 1.3 Similarity / 44 \\
                 1.4 Eigenvectors / 57 \\
                 Chapter 2 Unitary equivalence and normal matrices / 65
                 \\
                 2.0 Introduction / 65 \\
                 2.1 Unitary matrices / 66 \\
                 2.2 Unitary equivalence / 72 \\
                 2.3 Schur's unitary triangularization theorem / 79 \\
                 2.4 Some implications of Schur's theorem / 85 \\
                 2.5 Normal matrices / 100 \\
                 2.6 $Q R$ factorization and algorithm / 112 \\
                 Chapter 3 Canonical forms / 119 \\
                 3.0 Introduction / 119 \\
                 3.1 The Jordan canonical form: a proof / 121 \\
                 3.2 The Jordan canonical form: some observations and
                 applications / 129 \\
                 3.3 Polynomials and matrices: the minimal polynomial /
                 142 \\
                 3.4 Other canonical forms and factorizations / 150 \\
                 3.5 Triangular factorizations / 158 \\
                 Chapter 4 Hermitian and symmetric matrices / 167 \\
                 4.0 Introduction / 167 \\
                 4.1 Definitions, properties, and characterizations of
                 Hermitian matrices / 169 \\
                 4.2 Variational characterizations of eigenvalues of
                 Hermitian matrices / 176 \\
                 4.3 Some applications of the variational
                 characterizations / 181 \\
                 4.4 Complex symmetric matrices / 201 \\
                 4.5 Congruence and simultaneous diagonalization of
                 Hermitian and symmetric matrices / 218 \\
                 4.6 Consimilarity and condiagonalization / 244 \\
                 Chapter 5 Norms for vectors and matrices / 257 \\
                 5.0 Introduction / 257 \\
                 5.1 Defining properties of vector norms and inner
                 products / 259 \\
                 5.2 Examples of vector norms / 264 \\
                 5.3 Algebraic properties of vector norms / 268 \\
                 5.4 Analytic properties of vector norms / 269 \\
                 5.5 Geometric properties of vector norms / 281 \\
                 5.6 Matrix norms / 290 \\
                 5.7 Vector norms on matrices / 320 \\
                 5.8 Errors in inverses and solutions of linear systems
                 / 335 \\
                 Chapter 6 Location and perturbation of eigenvalues /
                 343 \\
                 6.0 Introduction / 343 \\
                 6.1 Ger{\v{s}}gorin discs / 344 \\
                 6.2 Ger{\v{s}}gorin discs --- a closer look / 353 \\
                 6.3 Perturbation theorems / 364 \\
                 6.4 Other inclusion regions / 378 \\
                 Chapter 7 Positive definite matrices / 391 \\
                 7.0 Introduction / 391 \\
                 7.1 Definitions and properties / 396 \\
                 7.2 Characterizations / 402 \\
                 7.3 The polar form and the singular value decomposition
                 / 411 \\
                 7.4 Examples and applications of the singular value
                 decomposition / 427 \\
                 7.5 The Schur product theorem / 455 \\
                 7.6 Congruence: products and simultaneous
                 diagonalization / 464 \\
                 7.7 The positive semidefinite ordering / 469 \\
                 7.8 Inequalities for positive definite matrices / 476
                 \\
                 Chapter 8 Nonnegative matrices / 487 \\
                 8.0 Introduction / 487 \\
                 8.1 Nonnegative matrices --- inequalities and
                 generalities / 490 \\
                 8.2 Positive matrices / 495 \\
                 8.3 Nonnegative matrices / 503 \\
                 8.4 Irreducible nonnegative matrices / 507 \\
                 8.5 Primitive matrices / 515 \\
                 8.6 A general limit theorem / 524 \\
                 8.7 Stochastic and doubly stochastic matrices / 526 \\
                 Appendices \\
                 A Complex numbers / 531 \\
                 B Convex sets and functions / 533 \\
                 C The fundamental theorem of algebra / 537 \\
                 D Continuous dependence of the zeroes of a polynomial
                 on its coefficients / 539 \\
                 E Weierstrass's theorem / 541 \\
                 References / 543 \\
                 Notation / 547 \\
                 Index / 549",
}

@Book{Horn:2012:MA,
  author =       "Roger A. Horn and Charles R. (Charles Royal) Johnson",
  title =        "Matrix Analysis",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "xviii + 643",
  year =         "2012",
  DOI =          "https://doi.org/10.1017/CBO9781139020411",
  ISBN =         "0-521-83940-8 (hardcover), 0-521-54823-3 (paperback),
                 1-283-74139-3, 1-139-77904-4, 1-139-77600-2 (e-book),
                 1-139-02041-2 (e-book)",
  ISBN-13 =      "978-0-521-83940-2 (hardcover), 978-0-521-54823-6
                 (paperback), 978-1-283-74139-2, 978-1-139-77904-3,
                 978-1-139-77600-4 (e-book), 978-1-139-02041-1
                 (e-book)",
  LCCN =         "QA188 .H66 2012",
  bibdate =      "Thu Nov 20 09:13:05 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
  abstract =     "The thoroughly revised and updated second edition of
                 this acclaimed text has several new and expanded
                 sections and more than 1,100 exercises.",
  acknowledgement = ack-nhfb,
  subject =      "Matrices; MATHEMATICS; Algebra; Abstract; Matrices",
  tableofcontents = "Frontmatter / i--vi \\
                 Contents / vii--x \\
                 Preface to the Second Edition / xi--xiv \\
                 Preface to the First Edition / xv--xviii \\
                 0. Review and Miscellanea / 1--42 \\
                 1. Eigenvalues, Eigenvectors, and Similarity / 43--82
                 \\
                 2. Unitary Similarity and Unitary Equivalence / 83--162
                 \\
                 3. Canonical Forms for Similarity and Triangular
                 Factorizations / 163--224 \\
                 4. Hermitian Matrices, Symmetric Matrices, and
                 Congruences / 225--312 \\
                 5. Norms for Vectors and Matrices / 313--386 \\
                 6. Location and Perturbation of Eigenvalues / 387--424
                 \\
                 7. Positive Definite and Semidefinite Matrices /
                 425--516 \\
                 8. Positive and Nonnegative Matrices / 517--554 \\
                 Appendix A. Complex Numbers / 555--556 \\
                 Appendix B. Convex Sets and Functions / 557--560 \\
                 Appendix C. The Fundamental Theorem of Algebra /
                 561--562 \\
                 Appendix D. Continuity of Polynomial Zeroes and Matrix
                 Eigenvalues / 563--564 \\
                 Appendix E. Continuity, Compactness, and Weierstrass's
                 Theorem / 565--566 \\
                 Appendix F. Canonical Pairs / 567--570 \\
                 References / 571--574 \\
                 Notation / 575--578 \\
                 Hints for Problems / 579--606 \\
                 Index / 607--643",
}

@Book{Householder:1964:TMN,
  author =       "Alston S. Householder",
  title =        "The Theory of Matrices in Numerical Analysis",
  publisher =    "Blaisdell Publishing Co. Ginn and Co.",
  address =      "New York / Toronto / London",
  pages =        "xi + 257",
  year =         "1964",
  LCCN =         "QA263 .H67",
  MRclass =      "65.35",
  MRnumber =     "0175290 (30 \#5475)",
  MRreviewer =   "R. S. Varga",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-date =  "1904--",
}

@Book{Householder:1972:LNA,
  author =       "A. S. Householder",
  title =        "Lectures on Numerical Algebra",
  publisher =    pub-MAA,
  address =      pub-MAA:adr,
  pages =        "iii + 250 + vii",
  year =         "1972",
  LCCN =         "QA155 .H67",
  MRclass =      "65-02 (15A60)",
  MRnumber =     "0408186 (53 \#11952)",
  MRreviewer =   "John Todd",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Notes on lectures given at the June 19--July 28, 1972,
                 MAA Summer Seminar, Williams College, Williamstown, MA,
                 USA.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Householder:1975:TMN,
  author =       "Alston Scott Householder",
  title =        "The Theory of Matrices in Numerical Analysis",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 257",
  year =         "1975",
  ISBN =         "0-486-61781-5",
  ISBN-13 =      "978-0-486-61781-7",
  LCCN =         "QA188 .H67 1975",
  bibdate =      "Sun Nov 23 09:13:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1904--",
  remark =       "Originally published by Blaisdell Pub. Co., New York.
                 Previous edition classed, QA263 .H67 (class number
                 shift).",
  subject =      "Matrices; Numerical analysis",
  tableofcontents = "1. Some Basic Identities and Inequalities // 1.0
                 Objectives; Notation / 1 \\
                 1.1 Elementary Matrices / 3 \\
                 1.2 Some Factorizations / 4 \\
                 1.3 Projections, and the General Reciprocal / 8 \\
                 1.4 Some Determinantal Identities / 10 \\
                 1.5 The Lanczos Algorithm for Tridiagonalization / 17
                 \\
                 1.6 Orthogonal Polynomials / 24 \\
                 References / 27 \\
                 Problems and Exercises / 29 \\
                 2. Norms, Bounds, and Convergence // 2.0 The Notion of
                 a Norm / 37 \\
                 2.1 Convex Sets and Convex Bodies / 38 \\
                 2.2 Norms and Bounds / 39 \\
                 2.3 Norms, Bounds, and Spectral Radii / 45 \\
                 2.4 Nonnegative Matrices / 48 \\
                 2.5 Convergence; Functions of Matrices / 53 \\
                 References / 55 \\
                 Problems and Exercises / 57 \\
                 3. Localization Theorems and Other Inequalities // 3.0
                 Basic Definitions / 64 \\
                 3.1 Exclusion Theorems / 65 \\
                 3.2 Inclusion and Separation Theorems / 70 \\
                 3.3 Minimax Theorems and the Field of Values / 74 \\
                 3.4 Inequalities of Wielandt and Kantrovich / 81 \\
                 References / 84 \\
                 Problems and Exercises / 85 \\
                 4. The Solution of Linear Systems: Methods of
                 Successive Approximation // 4.0 Direct Methods and
                 Others / 91 \\
                 4.1 The Inversion of Matrices / 94 \\
                 4.2 Methods of Projection / 98 \\
                 4.3 Norm-Reducing Methods / 103 \\
                 References / 115 \\
                 Problems and Exercises / 116 \\
                 5. Direct Methods of Inversion // 5.0 Uses of the
                 Inverse / 122 \\
                 5.1 The Method of Modification / 123 \\
                 5.2 Triangularization / 125 \\
                 5.3 A More General Formulation / 131 \\
                 5.4 Orthogonal Triangularization / 133 \\
                 5.5 Orthogonalization / 134 \\
                 5.6 Orthogonalization and Projection / 137 \\
                 5.7 The Method of Conjugate Gradients / 139 \\
                 References / 141 \\
                 Problems and Exercises / 142 \\
                 6. Proper Values and Vectors: Normalization and
                 Reduction of the Matrix // 6.0 Purpose of Normalization
                 / 147 \\
                 6.1 The Method of Krylov / 149 \\
                 6.2 The Weber--Voetter Method / 151 \\
                 6.3 The Method of Danilevskii / 156 \\
                 6.4 The Hessenberg and the Lanczos Reductions / 158 \\
                 6.5 Proper Values and Vectors / 163 \\
                 6.6 The Method of Samuelson and Bryan / 165 \\
                 6.7 The Method of Leverrier / 166 \\
                 6.8 Deflation / 168 \\
                 References / 172 \\
                 Problems and Exercises / 172 \\
                 7. Proper Values and Vectors: Successive Approximation
                 // 7.0 Methods of Successive Approximation / 178 \\
                 7.1 The Method of Jacobi / 179 \\
                 7.2 The Method of Collar and Jahn / 181 \\
                 7.3 Powers of a Matrix / 182 \\
                 7.4 Simple Iteration (the Power Method) / 187 \\
                 7.5 Multiple Roots and Principal Vectors / 190 \\
                 7.6 Staircase Iteration (Treppeniteration) / 191 \\
                 7.7 The $L R$-Transformation / 194 \\
                 7.8 Bi-iteration / 196 \\
                 7.9 The $Q R$-Transformation / 197 \\
                 References / 198 \\
                 Problems and Exercises / 199 \\
                 Bibliography / 203 \\
                 Index / 249",
}

@Book{Householder:2006:TMN,
  author =       "Alston Scott Householder",
  title =        "The Theory of Matrices in Numerical Analysis",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Dover",
  pages =        "xi + 257",
  year =         "2006",
  ISBN =         "0-486-44972-6 (paperback)",
  ISBN-13 =      "978-0-486-44972-2 (paperback)",
  LCCN =         "QA188 .H67 2006",
  bibdate =      "Sun Nov 23 09:13:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0634/2005054775-d.html",
  abstract =     "Suitable for advanced undergraduates and graduate
                 students, this text explores aspects of matrix theory
                 that are most useful in developing and appraising
                 computational methods for solving systems of linear
                 equations and for finding characteristic roots. An
                 introductory chapter covers the Lanczos algorithm,
                 orthogonal polynomials, and determinantal identities.
                 Succeeding chapters examine norms, bounds and
                 convergence; localization theorems and other
                 inequalities; and methods of solving systems of linear
                 equations. The final chapters illustrate mathematical
                 principles underlying linear equations and their
                 interrelationships, including methods of successive
                 approximation, direct methods of inversion,
                 normalization and reduction of the matrix, and proper
                 values and vectors.",
  acknowledgement = ack-nhfb,
  author-dates = "1904--",
  remark =       "Originally published: New York: Blaisdell Pub. Co.,
                 1964.",
  subject =      "Matrices; Numerical analysis",
}

@Book{Huppert:1996:HWM,
  editor =       "Bertram Huppert and Hans Schneider",
  title =        "{Helmut Wielandt: Mathematische werke = Mathematical
                 Works}. {Linear} algebra and analysis",
  volume =       "2",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  pages =        "xx + 632",
  year =         "1996",
  ISBN =         "3-11-012453-X (hardcover vol. 2), 3-11-012452-1 (vol.
                 2)",
  ISBN-13 =      "978-3-11-012453-8 (hardcover vol. 2),
                 978-3-11-012452-1 (vol. 2)",
  LCCN =         "QA3 .W52 1996",
  bibdate =      "Fri Nov 21 12:32:36 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/i/ipsen-ilse-c-f.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  subject =      "Wielandt, Helmut; Gruppentheorie; Aufsatzsammlung;
                 Matrix (Mathematik); Matrizenrechnung",
  tableofcontents = "Editors' Preface / v \\
                 Curriculum vitae / vi \\
                 Ph.D. Students of Helmut Wielandt / viii \\
                 Antrittsrede [72] / x \\
                 English translation of [72] by Robert E. Molzon and
                 Peter M. Neumann / xiii \\
                 Preface to Volume 2 / xvi \\
                 Contributors to Wielandt's Mathematical Works (Volume
                 2) / xvii \\
                 Research Papers / 1 \\
                 Das Iterationsverfahren bei nicht selbstadjungierten
                 linearen Eigenwertaufgaben [7] / 3 \\
                 Commentary on [7] by Helmut Brakhage / 54 \\
                 Eigenwerttheorie [8] / 60 \\
                 {\"U}ber die Unbeschr{\"a}nktheit der Operatoren der
                 Quantenmechanik [9] / 74 \\
                 Ein Einschlie{\ss}ungssatz f{\"u}r charakteristische
                 Wurzeln normaler Matrizen [10] / 75 \\
                 Editor's note on [10] by Hans Schneider / 79 \\
                 Die Einschlie{\ss}ung von Eigenwerten normaler Matrizen
                 [11] / 80 \\
                 Zur Abgrenzung der selbstadjungierten Eigenwertaufgaben
                 I. R{\"a}ume endlicher Dimension [13] / 88 \\
                 Unzerlegbare, nicht negative Matrizen [14] / 100 \\
                 Commentary on [14] by Hans Schneider / 107 \\
                 Lineare Scharen von Matrizen mit reellen Eigenwerten
                 [15] / 114 \\
                 Commentary on [15] by Rajendra Bhatia; / 121 \\
                 {\"U}ber die Eigenwertaufgaben mit reellen diskreten
                 Eigenwerten [16] / 122 \\
                 Commentary on [16] by Joachim von Below / 129 \\
                 Zur Umkehrung des Abelschen Stetigkeitssatzes [18] /
                 133 \\
                 The Variation of the spectrum of a normal matrix (with
                 Alan J. Hoffman) [19] / 135 \\
                 Commentary on [19] by Earl R. Barnes / 138 \\
                 Commentary on [19] by Miroslav Fiedler / 141 \\
                 Commentary on [19] by Shmuel Friedland / 142 \\
                 Commentary on [19] by Alan J. Hoffman / 144 \\
                 Commentary on [19] by John A. Holbrook / 145 \\
                 Commentary on [19] by Ji-guang Sun / 149 \\
                 Editor's note on [19] by Hans Schneider / 151 \\
                 Pairs of normal matrices with property L [20] / 152 \\
                 Commentary on [20] by Hans Schneider / 154 \\
                 Inclusion theorems for eigenvalues [21] / 156 \\
                 Commentary on [21] by Chandler Davis / 160 \\
                 Commentary on [21] by Hans Schneider / 161 \\
                 Editor's note on [21] by Hans Schneider / 162 \\
                 Error bounds for eigenvalues of Hermitian integral
                 equations and infinite matrices [23] / 163 \\
                 Einschlie{\ss}ung von Eigenwerten Hermitescher Matrizen
                 nach dem Abschnittsverfahren [24] / 165 \\
                 An extremum property of sums of eigenvalues [26] / 172
                 \\
                 Commentary on [26] by Rajendra Bhatia / 177 \\
                 XX Contents Commentary on [26] by Shmuel Friedland /
                 180 \\
                 On eigenvalues of sums of normal matrices [27] / 182
                 \\
                 Commentary on [27] by Robert C. Thompson / 188 \\
                 Error bounds for eigenvalues of Symmetrie integral
                 equations [28] / 190 \\
                 On the matrix function $A X + X' A'$ (with Olga
                 Taussky) [49] / 212 \\
                 Linear relations between higher additive commutators
                 (with Olga Taussiy) [50] / 216 \\
                 On the role of the determinant in semigroups of
                 matrices (with Olga Taussky) [52] / 220 \\
                 A spectral characterization of stochastic matrices
                 (with Richard A. Brualdi) [57] / 228 \\
                 Commentary on [57] by Richard A. Brualdi / 234 \\
                 On the eigenvalues of A + B and AB [60] / 235 \\
                 Commentary on [60] by Hans Schneider / 238 \\
                 Nested bounds for the Perron root of a nonnegative
                 matrix (with Emeric Deutsch) [69] / 241 \\
                 Wielandt in Washington, DC, and Pasadena, CA, and
                 Commentaries on Wielandt's Papers [8], [15], [19],
                 [20], [21], [27], [28], [49], [50], [52] by Olga
                 Taussky / 258 \\
                 Wielandt's Characterization of the $F$-Function by
                 Reinhold Remmert / 265 \\
                 Lecture Notes / 269 \\
                 Topics in the analytic theory of matrices [81] / 271
                 \\
                 Commentary on [81] by George P. Barker / 353 \\
                 Commentary on Section 23 of [81] by Karl Gustafson /
                 356 \\
                 Mimeographed Research Reports, Aerodynamische
                 Versuchsanstalt G{\"o}ttingen / 369 \\
                 Beitr{\"a}ge zur mathematischen Behandlung komplexer
                 Eigenwertprobleme I. Abzahlung der Eigenwerte komplexer
                 Matrizen [75,1] / 371 \\
                 III. Das Iterationsverfahren in der Flatterrechung [75,
                 III] / 385 \\
                 IV. Konvergenzbeweis f{\"u}r das Iterationsverfahren
                 [75, IV] / 434 \\
                 V. Bestimmung h{\"o}herer Eigenwerte durch gebrochene
                 Iteration [75, V] / 441 \\
                 Commentary on [75, V] by Wilhelm Niethammer / 452 \\
                 Helmut Wielandt's Contributions to the Numerical
                 Solution of Complex Eigenvalue Problems by Ilse C. F.
                 Ipsen / 453 \\
                 A History of Inverse Iteration by Ilse C. F. Ipsen /
                 464 \\
                 Beitr{\"a}ge zur instation{\"a}ren
                 Tragfl{\"a}chentheorie X. Zur Integralgleichung von
                 Possio [76, X] / 473 \\
                 XI. Geschlossene L{\"o}sung der Integralgleichung von
                 Possio f{\"u}r den Fall eines nach hinten unendlich
                 tiefen Fl{\"u}gels [76, XI] / 486 \\
                 XII. Geschlossene L{\"o}sung der Integralgleichung von
                 Possio f{\"u}r den Fall eines nach vorn unendlich
                 tiefen Fl{\"u}gels [76, XII] / 502 \\
                 Biographical Notes / 517 \\
                 Issai Schur zum Ged{\"a}chtnis [70] / 519 \\
                 Erhard Schmidt [71] / 520 \\
                 Hellmuth Kneser in Memoriam [73] / 521 \\
                 Hellmuth Kneser (16.4.1898--23.8.1973) [74] / 524 \\
                 Appendix / 527 \\
                 Ausgew{\"a}hlte Fragen {\"u}ber Permutationsgruppen
                 [88] / 529 \\
                 Acknowledgements / 626 \\
                 Bibliography / 627",
}

@Book{Jacobson:1943:TR,
  author =       "Nathan Jacobson",
  title =        "The Theory of Rings",
  volume =       "II",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "vi + 150",
  year =         "1943",
  LCCN =         "QA247",
  MRclass =      "09.1X",
  MRnumber =     "0008601 (5,31f)",
  MRreviewer =   "C. Chevalley",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "American Mathematical Society Mathematical Surveys",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1910--1999",
}

@Book{Kaplansky:2003:LAG,
  author =       "Irving Kaplansky",
  title =        "Linear Algebra and Geometry: a Second Course",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Revised",
  pages =        "xiv + 143",
  year =         "2003",
  ISBN =         "0-8284-0279-5 (hardcover), 0-486-43233-5 (paperback)",
  ISBN-13 =      "978-0-8284-0279-8 (hardcover), 978-0-486-43233-5
                 (paperback)",
  LCCN =         "QA184.2 .K37 2003",
  MRclass =      "15.00, 50.00, 15-01, 15A63, 15A69, 15A21, 15A23,
                 51N10, 51N15, 51N20",
  MRnumber =     "2001037 (2004c:15001)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0614/2003048902-d.html",
  abstract =     "A prominent and influential mathematician who has
                 received numerous awards wrote this text to remedy a
                 common failing in teaching algebra: the neglect of
                 related instruction in geometry. Based on his many
                 years of experience as an instructor the University of
                 Chicago, author Irving Kaplansky presents a coherent
                 overview of the correlation between these two branches
                 of mathematics, illustrating his topics with an
                 abundance of examples, exercises, and proofs. Suitable
                 for both undergraduate and graduate courses. Unabridged
                 republication of the edition published by Chelsea
                 Publishing Company, New York, 1974.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1917--2006",
  remark =       "Originally published: 2nd ed. New York: Chelsea Pub.
                 Co., 1974.",
  subject =      "Algebras, Linear; Geometry",
  tableofcontents = "1 Inner Product Spaces \\
                 1-1 Definitions and Examples / 1 \\
                 1-2 The Direct Summand Theorem / 5 \\
                 1-3 Diagonalization / 7 \\
                 1-4 The Inertia Theorem / 10 \\
                 1-5 The Discriminant / 12 \\
                 1-6 Finite Fields / 14 \\
                 1-7 Witt's Cancellation Theorem / 17 \\
                 1-8 Hyperbolic Planes / 19 \\
                 1-9 Alternate Forms / 21 \\
                 1-10 Characteristic $2$: Symmetric Bilinear Forms / 23
                 \\
                 1-11 Witt's Theorem on Piecewise Equivalence / 25 \\
                 1-12 Characteristic $2$: Quadratic Forms / 27 \\
                 1-13 Hermitian Forms / 34 \\
                 1-14 Some Alternative Proofs / 38 \\
                 1-15 Infinite-Dimensional Inner Product Spaces / 39 \\
                 1-16 Forms Over Rings / 46 \\
                 2 Orthogonal Similarity \\
                 2-1 The Real Self-Adjoint Case / 57 \\
                 2-2 Unitary Spaces / 60 \\
                 2-3 Positivity and Polar Decomposition / 65 \\
                 2-4 The Real Case, Continued / 69 \\
                 2-5 Specht's Theorem / 71 \\
                 2-6 Remarks on Similarity / 73 \\
                 2-7 Orthogonal Similarity over Algebraically Closed
                 Fields / 77 \\
                 3 Geometry \\
                 3-1 Affine Planes / 83 \\
                 3-2 Inner Product Planes / 93 \\
                 3-3 Projective Planes / 97 \\
                 3-4 Projective Transformations / 101 \\
                 3-5 Duality / 104 \\
                 3-6 Cross Ratio and Harmonic Range / 105 \\
                 3-7 Conics / 113 \\
                 3-8 Higher Dimensional Spaces / 120 \\
                 3-9 Noncommutativity / 123 \\
                 3-10 Synthetic Foundations of Geometry / 124 \\
                 Appendix: Topological Aspects of Projective Spaces /
                 130 \\
                 Bibliography / 137 \\
                 Index / 141",
}

@Book{Karlin:1968:TP,
  author =       "Samuel Karlin",
  title =        "Total Positivity",
  publisher =    pub-STANFORD,
  address =      pub-STANFORD:adr,
  pages =        "xi + 576",
  year =         "1968",
  LCCN =         "QA331.5 .K3",
  bibdate =      "Fri Nov 21 09:06:29 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1923--2007",
  subject =      "Functions of real variables; Transformations
                 (Mathematics); Spline theory",
}

@Book{Kato:1966:PTL,
  author =       "Tosio Kat{\=o}",
  title =        "Perturbation Theory for Linear Operators",
  volume =       "132",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xix + 592",
  year =         "1966",
  LCCN =         "QA320 .K33",
  bibdate =      "Sun Nov 23 09:24:47 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Die Grundlehren der mathematischen Wissenschaften in
                 Einseldarstellungen",
  acknowledgement = ack-nhfb,
  author-dates = "1917--",
  subject =      "Linear operators; Perturbation (Mathematics)",
}

@Book{Kato:1976:PTL,
  author =       "Tosio Kat{\=o}",
  title =        "Perturbation Theory for Linear Operators",
  volume =       "132",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xxi + 619",
  year =         "1976",
  ISBN =         "0-387-07558-5",
  ISBN-13 =      "978-0-387-07558-7",
  LCCN =         "QA329.2 .K37 1976",
  MRclass =      "47-XX",
  MRnumber =     "0407617 (53 \#11389)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Grundlehren der Mathematischen Wissenschaften",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1917--",
  tableofcontents = "Introduction \\
                 Operator theory in finite-dimensional vector spaces \\
                 Vector spaces and normed vector spaces / 1 \\
                 Linear forms and the adjoint space / 10 \\
                 Linear operators / 16 \\
                 Analysis with operators / 25 \\
                 The eigenvalue problem / 34 \\
                 Operators in unitary spaces / 47 \\
                 Perturbation theory in a finite-dimensional space / 62
                 \\
                 Analytic perturbation of eigenvalues / 63 \\
                 Perturbation series / 74 \\
                 Convergence radii and error estimates / 88 \\
                 Similarity transformations of the eigenspaces and
                 eigenvectors / 98 \\
                 Non-analytic perturbations / 106 \\
                 Perturbation of symmetric operators / 120 \\
                 Introduction to the theory of operators in Banach
                 spaces \\
                 Banach spaces / 127 \\
                 Linear operators in Banach spaces / 142 \\
                 Bounded operators / 149 \\
                 Compact operators / 157 \\
                 Closed operators / 163 \\
                 Resolvents and spectra / 172 \\
                 Stability theorems \\
                 Stability of closedness and bounded invertibility / 189
                 \\
                 Generalized convergence of closed operators / 197 \\
                 Perturbation of the spectrum / 208 \\
                 Pairs of closed linear manifolds / 218 \\
                 Stability theorems for semi-Fredholm operators / 229
                 \\
                 Degenerate perturbations / 244 \\
                 Operators in Hilbert spaces \\
                 Hilbert space / 251 \\
                 Bounded operators in Hilbert spaces / 256 \\
                 Unbounded operators in Hilbert spaces / 267 \\
                 Perturbation of selfadjoint operators / 287 \\
                 The Schr{\"o}dinger and Dirac operators / 297 \\
                 Sesquilinear forms in Hilbert spaces and associated
                 operators \\
                 Sesquilinear and quadratic forms / 308 \\
                 The representation theorems / 322 \\
                 Perturbation of sesquilinear forms and the associated
                 operators / 336 \\
                 Quadratic forms and the Schr{\"o}dinger operators / 343
                 \\
                 The spectral theorem and perturbation of spectral
                 families / 353 \\
                 Analytic perturbation theory \\
                 Analytic families of operators / 365 \\
                 Holomorphic families of type (A) / 375 \\
                 Selfadjoint holomorphic families / 385 \\
                 Holomorphic families of type (B) / 393 \\
                 Further problems of analytic perturbation theory / 413
                 \\
                 Eigenvalue problems in the generalized form / 416 \\
                 Asymptotic perturbation theory \\
                 Strong convergence in the generalized sense / 427 \\
                 Asymptotic expansions / 441 \\
                 Generalized strong convergence of sectorial operators /
                 453 \\
                 Asymptotic expansions for sectorial operators / 463 \\
                 Spectral concentration / 473 \\
                 Perturbation theory for semigroups of operators \\
                 One-parameter semigroups and groups of operators / 479
                 \\
                 Perturbation of semigroups / 497 \\
                 Approximation by discrete semigroups / 509 \\
                 Perturbation of continuous spectra and unitary
                 equivalence \\
                 The continuous spectrum of a selfadjoint operator / 516
                 \\
                 Perturbation of continuous spectra / 525 \\
                 Wave operators and the stability of absolutely
                 continuous spectra / 529 \\
                 Existence and completeness of wave operators / 537 \\
                 A stationary method / 553 \\
                 Bibliography / 583 \\
                 Supplementary Bibliography / 596 \\
                 Notation index / 606 \\
                 Author index / 608 \\
                 Subject index / 612",
}

@Book{Kato:1984:PTL,
  author =       "Tosio Kat{\=o}",
  title =        "Perturbation Theory for Linear Operators",
  volume =       "132",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second [corrected]",
  pages =        "xxi + 619",
  year =         "1984",
  ISBN =         "3-540-07558-5 (Berlin), 0-387-07558-5 (New York)",
  ISBN-13 =      "978-3-540-07558-5 (Berlin), 978-0-387-07558-7 (New
                 York)",
  LCCN =         "QA329.2 .K37 1984",
  bibdate =      "Sun Nov 23 09:24:47 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Grundlehren der mathematischen Wissenschaften in
                 Einzeldarstellungen mit besonderer Ber{\"u}cksichtigung
                 der Anwendungsgebiete",
  acknowledgement = ack-nhfb,
  author-dates = "1917--",
}

@Book{Kato:1995:PTL,
  author =       "Tosio Kat{\=o}",
  title =        "Perturbation Theory for Linear Operators",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxi + 619",
  year =         "1995",
  ISBN =         "3-540-58661-X",
  ISBN-13 =      "978-3-540-58661-6",
  LCCN =         "QA329.2 .K37 1995",
  bibdate =      "Sun Nov 23 09:24:47 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Classics in mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0815/94039131-b.html",
  acknowledgement = ack-nhfb,
  author-dates = "1917--",
  remark =       "``Reprint of the 1980 edition.''. Originally
                 published: 2nd ed. Berlin; New York: Springer-Verlag,
                 1976 (1980 printing). (Grundlehren der mathematischen
                 Wissenschaften in Einzeldarstellungen mit besonderer
                 Ber{\"u}cksichtigung der Anwendungsgebiete; Bd. 132).",
  subject =      "Linear operators; Perturbation (Mathematics)",
}

@TechReport{Kellogg:1971:TMT,
  author =       "R. Bruce Kellogg",
  title =        "Topics in Matrix Theory",
  type =         "Lecture notes",
  number =       "71.04",
  institution =  "Chalmers Institute of Technology and the University of
                 G{\"o}teborg",
  address =      "G{\"o}teborg, Sweden",
  pages =        "76",
  year =         "1971",
  bibdate =      "Fri Nov 21 09:09:13 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
}

@Book{Konig:1936:TEU,
  author =       "D{\'e}nes K{\H{o}}nig",
  title =        "{Theorie der endlichen und unendlichen Graphen:
                 kombinatorische Topologie der Streckenkomplexe}.
                 (German) [{Theory} of finite and infinite graphs:
                 combinatorial topology of route [??] complexes]",
  volume =       "16",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  pages =        "xi + 258",
  year =         "1936",
  LCCN =         "QA611 .K6",
  bibdate =      "Fri Nov 21 09:14:55 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Mathematik und ihre Anwendungen in Monographien und
                 Lehrb{\=u}chern",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1884--1944",
  language =     "German",
  remark =       "Yes, the author's family name is spelled with a long
                 Hungarian accent, instead of the usual German umlaut.",
}

@Book{Konig:1950:TEU,
  author =       "D{\'e}nes K{\H{o}}nig",
  title =        "{Theorie der endlichen und unendlichen Graphen}.
                 (German) [{Theory} of finite and infinite graphs]",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  pages =        "348",
  year =         "1950",
  LCCN =         "QA611 .K6 1950",
  bibdate =      "Fri Nov 21 09:14:55 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1884--1944",
  language =     "German",
  remark =       "Yes, the author's family name is spelled with a long
                 Hungarian accent, instead of the usual German umlaut.",
}

@Book{Konig:1954:TEU,
  author =       "D{\'e}nes K{\H{o}}nig",
  title =        "{Theorie der endlichen und unendlichen Graphen}.
                 (German) [{Theory} of finite and infinite graphs]",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  pages =        "348",
  year =         "1954",
  LCCN =         "QA611 .K6 1954",
  bibdate =      "Fri Nov 21 09:14:55 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1884--1944",
  language =     "German",
  remark =       "Yes, the author's family name is spelled with a long
                 Hungarian accent, instead of the usual German umlaut.",
}

@Book{Konig:1990:TFI,
  author =       "D{\'e}nes K{\H{o}}nig",
  title =        "Theory of Finite and Infinite Graphs",
  publisher =    pub-BIRKHAUSER-BOSTON,
  address =      pub-BIRKHAUSER-BOSTON:adr,
  pages =        "vi + 426",
  year =         "1990",
  DOI =          "https://doi.org/10.1007/978-1-4684-8971-2",
  ISBN =         "3-7643-3389-8 (Basel), 0-8176-3389-8 (Boston),
                 1-4684-8971-2 (e-book)",
  ISBN-13 =      "978-3-7643-3389-8 (Basel), 978-0-8176-3389-9 (Boston),
                 978-1-4684-8971-2 (e-book)",
  LCCN =         "QA166 .K6613 1990",
  MRclass =      "01A75 (05Cxx)",
  MRnumber =     "1035708 (91f:01026)",
  MRreviewer =   "Robin J. Wilson",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Translated from the German by Richard McCoart. With a
                 commentary by W. T. Tutte and a biographical sketch by
                 T. Gallai.",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht003460259.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0695.05015",
  ZMnumber =     "0695.05015",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1884--1944",
  remark =       "Yes, the author's family name is spelled with a long
                 Hungarian accent, instead of the usual German umlaut.",
  subject =      "K{\H{o}}nig, D. (D{\'e}nes),; Graph theory;
                 Mathematics; Combinatorics; History of Mathematical
                 Sciences; Mathematical Logic and Foundations; Graphes,
                 Th{\'e}orie des; Graphentheorie; Graph theory",
  tableofcontents = "Commentary / W. T. Tutte \\
                 Theory of Finite and Infinite Graphs / D. K{\H{o}}nig /
                 45 \\
                 D{\'e}nes K{\H{o}}nig: A Biographical Sketch / T.
                 Gallai / 423",
}

@Book{Kowalsky:1963:LAG,
  author =       "Hans-Joachim Kowalsky",
  title =        "{Lineare Algebra}. ({German}) [Linear Algebra]",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  pages =        "340",
  year =         "1963",
  LCCN =         "????",
  bibdate =      "Fri Nov 21 09:28:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Book{Kowalsky:1967:LAG,
  author =       "Hans-Joachim Kowalsky",
  title =        "{Lineare Algebra}. ({German}) [Linear Algebra]",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  edition =      "Third",
  pages =        "342",
  year =         "1967",
  LCCN =         "QA251 .K68 1967",
  bibdate =      "Fri Nov 21 09:28:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Book{Kowalsky:1969:LAG,
  author =       "Hans-Joachim Kowalsky",
  title =        "{Lineare Algebra}. ({German}) [Linear Algebra]",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  edition =      "Fourth",
  pages =        "342",
  year =         "1969",
  LCCN =         "????",
  bibdate =      "Fri Nov 21 09:28:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  language =     "German",
}

@Book{Kowalsky:1970:LAG,
  author =       "Hans-Joachim Kowalsky",
  title =        "{Lineare Algebra}. ({German}) [Linear Algebra]",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  edition =      "Fifth",
  pages =        "341",
  year =         "1970",
  LCCN =         "QA251 .K68 1970",
  bibdate =      "Fri Nov 21 09:28:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Book{Kowalsky:1979:LAG,
  author =       "Hans-Joachim Kowalsky",
  title =        "{Lineare Algebra}. ({German}) [Linear Algebra]",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  edition =      "Ninth",
  pages =        "367",
  year =         "1979",
  ISBN =         "3-11-008164-4, 3-11-007835-X",
  ISBN-13 =      "978-3-11-008164-0, 978-3-11-007835-0",
  LCCN =         "QH 140",
  bibdate =      "Fri Nov 21 09:28:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Book{Kowalsky:1995:LAG,
  author =       "Hans-Joachim Kowalsky and Gerhard O. Michler",
  title =        "{Lineare Algebra}. ({German}) [Linear Algebra]",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  edition =      "Tenth",
  pages =        "xiv + 399",
  year =         "1995",
  ISBN =         "3-11-014501-4 (paperback), 3-11-014502-2 (hardcover)",
  ISBN-13 =      "978-3-11-014501-4 (paperback), 978-3-11-014502-1
                 (hardcover)",
  LCCN =         "QA184 .K72 1995",
  bibdate =      "Fri Nov 21 09:28:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht006543541.pdf;
                 http://www.zentralblattmath.org/zmath/en/search/?an=0827.15001",
  acknowledgement = ack-nhfb,
  author-dates = "Hans-Joachim Kowalsky (1921--)",
  language =     "German",
  tableofcontents = "Vorwort / v \\
                 Einleitung / vii \\
                 Symbolverzeichnis / xii \\
                 1 Grundbegriffe / 1 \\
                 1.1 Mengentheoretische Grundbegriffe / 1 \\
                 1.2 Produktmengen und Relationen / 6 \\
                 1.3 Gruppen / 8 \\
                 1.4 K{\"o}rper und Ringe / 12 \\
                 1.5 Vektorr{\"a}ume / 15 \\
                 1.6 Lineare Gleichungssysteme / 20 \\
                 1.7 Aufgaben / 22 \\
                 2 Struktur der Vektorr{\"a}ume / 24 \\
                 2.1 Unterr{\"a}ume / 25 \\
                 2.2 Basis und Dimension / 28 \\
                 2.3 Direkte Summen und Struktursatz / 36 \\
                 2.4 Aufgaben / 42 \\
                 3 Lineare Abbildungen und Matrizen / 44 \\
                 3.1 Matrizen / 45 \\
                 3.2 Lineare Abbildungen / 54 \\
                 3.3 Matrix einer linearen Abbildung / 61 \\
                 3.4 Rang einer Matrix / 66 \\
                 3.5 {\"A}quivalenz und {\"A}hnlichkeit von Matrizen /
                 70 \\
                 3.6 Abbildungsr{\"a}ume und Dualraum / 72 \\
                 3.7 Aufgaben / 77 \\
                 4 Gau{\ss}-Algorithmus und Gleichungssysteme / 81 \\
                 4.1 Gau{\ss}-Algorithmus / 81 \\
                 4.2 L{\"o}sungsverfahren f{\"u}r Gleichungssysteme / 92
                 \\
                 4.3 Aufgaben $\cdot$ $\cdot$ / 98 \\
                 5 Determinanten / 101 \\
                 5.1 Permutationen / 101 \\
                 5.2 Multilinearformen / 104 \\
                 5.3 Determinanten von Endomorphismen und Matrizen / 108
                 \\
                 5.4 Rechenregeln f{\"u}r Determinanten von Matrizen /
                 112 \\
                 5.5 Anwendungen / 119 \\
                 5.6 Aufgaben / 121 \\
                 6 Eigenwerte und Eigenvektoren / 124 \\
                 6.1 Charakteristisches Polynom und Eigenwerte / 124 \\
                 6.2 Diagonalisierbarkeit von Matrizen / 132 \\
                 6.3 Aufgaben / 137 \\
                 7 Euklidische und unit{\"a}re Vektorr{\"a}ume / 139 \\
                 7.1 Skalarprodukte und Hermitesche Formen / 139 \\
                 7.2 Betrag und Orthogonalit{\"a}t / 145 \\
                 7.3 Orthonormalisierungsverfahren / 151 \\
                 7.4 Adjungierte Abbildungen und normale Endomorphismen
                 / 156 \\
                 7.5 Orthogonale und unit{\"a}re Abbildungen / 164 \\
                 7.6 Hauptachsentheorem / 169 \\
                 7.7 Aufgaben / 175 \\
                 8 Anwendungen in der affinen Geometrie / 179 \\
                 8.1 Affine R{\"a}ume / 179 \\
                 8.2 Affine Abbildungen / 185 \\
                 8.3 Kongruenzen und Drehungen / 193 \\
                 8.4 Quadriken / 202 \\
                 8.5 Aufgaben / 214 \\
                 9 Ringe und Moduln / 217 \\
                 9.1 Ideale und Restklassenringe / 217 \\
                 9.2 Moduln / 221 \\
                 9.3 Kommutative Diagramme und exakte Folgen / 228 \\
                 9.4 Endlich erzeugte und freie Moduln / 230 \\
                 9.5 Matrizen und lineare Abbildungen freier Moduln /
                 236 \\
                 9.6 Direkte Produkte und lineare Abbildungen / 238 \\
                 9.7 Aufgaben / 252 \\
                 10 Multilineare Algebra / 254 \\
                 10.1 Multilineare Abbildungen und Tensorprodukte / 254
                 \\
                 10.2 Tensorprodukte von linearen Abbildungen / 262 \\
                 10.3 Ringerweiterungen und Tensorprodukte / 264 \\
                 10.4 {\"A}u{\ss}ere Potenzen und alternierende
                 Abbildungen / 266 \\
                 10.5 Determinante eines Endomorphismus / 272 \\
                 10.6 Tensoralgebra und {\"a}u{\ss}ere Algebra / 276 \\
                 10.7 Aufgaben / 278 \\
                 11 Moduln {\"u}ber Hauptidealringen / 280 \\
                 11.1 Eindeutige Faktorzerlegung in Hauptidealringen /
                 281 \\
                 11.2 Torsionsmodul eines endlich erzeugten Moduls / 289
                 \\
                 11.3 Prim{\"a}rzerlegung / 293 \\
                 11.4 Struktursatz f{\"u}r endlich erzeugte Moduln / 296
                 \\
                 11.5 Elementarteiler von Matrizen / 301 \\
                 11.6 Aufgaben / 321 \\
                 12 Normalformen einer Matrix / 324 \\
                 12.1 Invariante Unterr{\"a}ume als Moduln {\"u}ber
                 einem Polynomring / 324 \\
                 12.2 Matrizen und direkte Zerlegung / 326 \\
                 12.3 Rationale kanonische Form / 329 \\
                 12.4 Jordansche Normalform / 335 \\
                 12.5 Berechnungsverfahren f{\"u}r die Normalformen /
                 339 \\
                 12.6 Aufgaben / 349 \\
                 A Computeralgebrasysteme / 352 \\
                 B L{\"o}sungen der Aufgaben / 364 \\
                 B.1 L{\"o}sungen zu Kapitel 1 / 364 \\
                 B.2 L{\"o}sungen zu Kapitel 2 / 365 \\
                 B.3 L{\"o}sungen zu Kapitel 3 / 366 \\
                 B.4 L{\"o}sungen zu Kapitel 4 / 370 \\
                 B.5 L{\"o}sungen zu Kapitel 5 / 372 \\
                 B.6 L{\"o}sungen zu Kapitel 6 / 374 \\
                 B.7 L{\"o}sungen zu Kapitel 7 / 375 \\
                 B.8 L{\"o}sungen zu Kapitel 8 / 378 \\
                 B.9 L{\"o}sungen zu Kapitel 9 / 381 \\
                 B.10 L{\"o}sungen zu Kapitel 10 / 383 \\
                 B.11 L{\"o}sungen zu Kapitel 11 / 385 \\
                 B.12 L{\"o}sungen zu Kapitel 12 / 388 \\
                 Literatur / 393 \\
                 Index / 395",
}

@Book{Kowalsky:1998:LAG,
  author =       "Hans-Joachim Kowalsky and Gerhard O. Michler",
  title =        "{Lineare Algebra}. ({German}) [Linear Algebra]",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  edition =      "Eleventh",
  pages =        "xiv + 401",
  year =         "1998",
  ISBN =         "3-11-016185-0 (paperback), 3-11-016186-9 (hardcover)",
  ISBN-13 =      "978-3-11-016185-4 (paperback), 978-3-11-016186-1
                 (hardcover)",
  LCCN =         "QA184 .K72 1998",
  bibdate =      "Fri Nov 21 09:28:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht008883781.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "GOM (1938--)",
  language =     "German",
  tableofcontents = "Vorworte / v \\
                 Einleitung / vii \\
                 Bezeichnungen und Symbole / xii \\
                 1 Grundbegriffe / 1 \\
                 1.1 Mengentheoretische Grundbegriffe / 1 \\
                 1.2 Produktmengen und Relationen / 6 \\
                 1.3 Gruppen / 8 \\
                 1.4 K{\"o}rper und Ringe / 12 \\
                 1.5 Vektorr{\"a}ume / 15 \\
                 1.6 Lineare Gleichungssysteme / 20 \\
                 1.7 Aufgaben / 21 \\
                 2 Struktur der Vektorr{\"a}ume / 23 \\
                 2.1 Unterr{\"a}ume / 24 \\
                 2.2 Basis und Dimension / 27 \\
                 2.3 Direkte Summen und Struktursatz / 36 \\
                 2.4 Aufgaben / 41 \\
                 3 Lineare Abbildungen und Matrizen / 43 \\
                 3.1 Matrizen / 44 \\
                 3.2 Lineare Abbildungen / 53 \\
                 3.3 Matrix einer linearen Abbildung / 60 \\
                 3.4 Rang einer Matrix / 65 \\
                 3.5 {\"A}quivalenz und {\"A}hnlichkeit von Matrizen /
                 69 \\
                 3.6 Abbildungsr{\"a}ume und Dualraum / 71 \\
                 3.7 Aufgaben / 76 \\
                 4 Gau{\ss}-Algorithmus und lineare Gleichungssysteme /
                 80 \\
                 4.1 Gau{\ss}-Algorithmus / 80 \\
                 4.2 L{\"o}sungsverfahren f{\"u}r Gleichungssysteme / 90
                 \\
                 4.3 Aufgaben / 96 \\
                 5 Determinanten / 99 \\
                 5.1 Permutationen / 99 \\
                 5.2 Multilinearformen / 102 \\
                 5.3 Determinanten von Endomorphismen und Matrizen / 106
                 \\
                 5.4 Rechenregeln f{\"u}r Determinanten von Matrizen /
                 110 \\
                 5.5 Anwendungen / 117 \\
                 5.6 Aufgaben / 118 \\
                 6 Eigenwerte und Eigenvektoren / 121 \\
                 6.1 Charakteristisches Polynom und Eigenwerte / 121 \\
                 6.2 Diagonalisierbarkeit von Matrizen / 129 \\
                 6.3 Aufgaben / 134 \\
                 7 Euklidische und unit{\"a}re Vektorr{\"a}ume / 136 \\
                 7.1 Skalarprodukte und Hermitesche Formen / 136 \\
                 7.2 Betrag und Orthogonalit{\"a}t / 142 \\
                 7.3 Orthonormalisierungsverfahren / 147 \\
                 7.4 Adjungierte Abbildungen und normale Endomorphismen
                 / 152 \\
                 7.5 Orthogonale und unit{\"a}re Abbildungen / 161 \\
                 7.6 Hauptachsentheorem f{\"u}r Hermitesche und
                 symmetrische Matrizen / 166 \\
                 7.7 Aufgaben / 173 \\
                 8 Anwendungen in der Geometrie / 177 \\
                 8.1 Affine R{\"a}ume / 177 \\
                 8.2 Affine Abbildungen / 183 \\
                 8.3 Kongruenzen und Drehungen / 187 \\
                 8.4 Projektive R{\"a}ume / 198 \\
                 8.5 Projektivit{\"a}ten / 205 \\
                 8.6 Projektive Quadriken / 208 \\
                 8.7 Affine Quadriken / 214 \\
                 8.8 Aufgaben / 224 \\
                 9 Ringe und Moduln / 227 \\
                 9.1 Ideale und Restklassenringe / 227 \\
                 9.2 Moduln / 231 \\
                 9.3 Kommutative Diagramme und exakte Folgen / 238 \\
                 9.4 Endlich erzeugte und freie Moduln / 240 \\
                 9.5 Matrizen und lineare Abbildungen freier Moduln /
                 246 \\
                 9.6 Direkte Produkte und lineare Abbildungen / 248 \\
                 9.7 Aufgaben / 259 \\
                 10 Multilineare Algebra / 262 \\
                 10.1 Multilineare Abbildungen und Tensorprodukte / 262
                 \\
                 10.2 Tensorprodukte von linearen Abbildungen / 270 \\
                 10.3 Ringerweiterungen und Tensorprodukte / 272 \\
                 10.4 {\"A}u{\ss}ere Potenzen und alternierende
                 Abbildungen / 275 \\
                 10.5 Determinante eines Endomorphismus / 280 \\
                 10.6 Aufgaben / 284 \\
                 11 Moduln {\"u}ber Hauptidealringen / 286 \\
                 11.1 Eindeutige Faktorzerlegung in Hauptidealringen /
                 287 \\
                 11.2 Torsionsmodul eines endlich erzeugten Moduls / 295
                 \\
                 11.3 Prim{\"a}rzerlegung / 299 \\
                 11.4 Struktursatz f{\"u}r endlich erzeugte Moduln / 302
                 \\
                 11.5 Elementarteiler von Matrizen / 307 \\
                 11.6 Aufgaben / 327 \\
                 12 Normalformen einer Matrix / 330 \\
                 12.1 Invariante Unterr{\"a}ume als Moduln {\"u}ber
                 einem Polynomring / 330 \\
                 12.2 Matrizen und direkte Zerlegung / 334 \\
                 12.3 Rationale kanonische Form / 336 \\
                 12.4 Jordansche Normalform / 340 \\
                 12.5 Berechnungsverfahren f{\"u}r die Normalformen /
                 342 \\
                 12.6 Aufgaben / 355 \\
                 A Hinweise zur Benutzung von Computeralgebrasystemen /
                 358 \\
                 B L{\"o}sungen der Aufgaben / 363 \\
                 B.1 L{\"o}sungen zu Kapitel 1 / 363 \\
                 B.2 L{\"o}sungen zu Kapitel 2 / 364 \\
                 B.3 L{\"o}sungen zu Kapitel 3 / 365 \\
                 B.4 L{\"o}sungen zu Kapitel 4 / 369 \\
                 B.5 L{\"o}sungen zu Kapitel 5 / 371 \\
                 B.6 L{\"o}sungen zu Kapitel 6 / 373 \\
                 B.7 L{\"o}sungen zu Kapitel 7 / 374 \\
                 B.8 L{\"o}sungen zu Kapitel 8 / 378 \\
                 B.9 L{\"o}sungen zu Kapitel 9 / 382 \\
                 B.10 L{\"o}sungen zu Kapitel 10 / 384 \\
                 B.11 L{\"o}sungen zu Kapitel 11 / 386 \\
                 B.12 L{\"o}sungen zu Kapitel 12 / 389 \\
                 Literatur / 393 \\
                 Index 395",
}

@Book{Kowalsky:2003:LAG,
  author =       "Hans-Joachim Kowalsky and Gerhard O. Michler",
  title =        "{Lineare Algebra}. ({German}) [Linear Algebra]",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  edition =      "Twelfth",
  pages =        "xv + 416",
  year =         "2003",
  DOI =          "https://doi.org/10.1515/9783110200041",
  ISBN =         "3-11-017963-6 (paperback), 3-11-020004-X (e-book)",
  ISBN-13 =      "978-3-11-017963-7 (paperback), 978-3-11-020004-1
                 (e-book)",
  LCCN =         "QA184 .K693 2003",
  bibdate =      "Fri Nov 21 09:28:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  URL =          "http://d-nb.info/968354416/04;
                 http://www.degruyter.com/doi/book/10.1515/9783110200041;
                 http://www.degruyter.com/viewbooktoc/product/36737;
                 http://www.reference-global.com/isbn/978-3-11-020004-1",
  acknowledgement = ack-nhfb,
  author-dates = "Hans-Joachim Kowalsky (1921--), Gerhard O. Michler
                 (1938--)",
  language =     "German",
  tableofcontents = "Vorwort / v \\
                 Einleitung / vii \\
                 Bezeichnungen und Symbole / xii \\
                 1 Grundbegriffe / 1 \\
                 1.1 Mengentheoretische Grundbegriffe / 1 \\
                 1.2 Produktmengen und Relationen / 6 \\
                 1.3 Gruppen / 8 \\
                 1.4 K{\"o}rper und Ringe / 12 \\
                 1.5 Vektorr{\"a}ume / 15 \\
                 1.6 Lineare Gleichungssysteme / 20 \\
                 1.7 Aufgaben / 21 \\
                 2 Struktur der Vektorr{\"a}ume / 23 \\
                 2.1 Unterr{\"a}ume / 24 \\
                 2.2 Basis und Dimension / 27 \\
                 2.3 Direkte Summen und Struktursatz / 36 \\
                 2.4 Aufgaben / 41 \\
                 3 Lineare Abbildungen und Matrizen / 43 \\
                 3.1 Matrizen / 44 \\
                 3.2 Lineare Abbildungen / 52 \\
                 3.3 Matrix einer linearen Abbildung / 60 \\
                 3.4 Rang einer Matrix / 64 \\
                 3.5 {\"A}quivalenz und {\"A}hnlichkeit von Matrizen /
                 67 \\
                 3.6 Abbildungsr{\"a}ume und Dualraum / 70 \\
                 3.7 Matrizen und direkte Zerlegung / 75 \\
                 3.8 Aufgaben / 76 \\
                 4 Gau{\ss}-Algorithmus und lineare Gleichungssysteme /
                 80 \\
                 4.1 Gau{\ss}-Algorithmus / 80 \\
                 4.2 L{\"o}sungsverfahren f{\"u}r Gleichungssysteme / 90
                 \\
                 4.3 Aufgaben / 96 \\
                 5 Determinanten / 99 \\
                 5.1 Permutationen / 99 \\
                 5.2 Multilinearformen / 102 \\
                 5.3 Determinanten von Endomorphismen und Matrizen / 106
                 \\
                 5.4 Rechenregeln f{\"u}r Determinanten von Matrizen /
                 110 \\
                 5.5 Anwendungen / 117 \\
                 5.6 Aufgaben / 118 \\
                 6 Eigenwerte und Eigenvektoren / 121 \\
                 6.1 Charakteristisches Polynom und Eigenwerte / 121 \\
                 6.2 Diagonalisierbarkeit von Matrizen / 128 \\
                 6.3 Jordansche Normalform / 132 \\
                 6.4 Anwendung der Jordanschen Normalform / 144 \\
                 6.5 Aufgaben / 148 \\
                 7 Euklidische und unit{\"a}re Vektorr{\"a}ume / 152 \\
                 7.1 Skalarprodukte und Hermitesche Formen / 152 \\
                 7.2 Betrag und Orthogonalit{\"a}t / 158 \\
                 7.3 Orthonormalisierungsverfahren / 164 \\
                 7.4 Adjungierte Abbildungen und normale Endomorphismen
                 / 169 \\
                 7.5 Orthogonale und unit{\"a}re Abbildungen / 178 \\
                 7.6 Hauptachsentheorem <, / 182 \\
                 7.7 Aufgaben / 190 \\
                 8 Anwendungen in der Geometrie / 194 \\
                 8.1 Affine R{\"a}ume / 194 \\
                 8.2 Affine Abbildungen / 200 \\
                 8.3 Kongruenzen und Drehungen / 204 \\
                 8.4 Projektive R{\"a}ume / 215 \\
                 8.5 Projektivit{\"a}ten / 222 \\
                 8.6 Projektive Quadriken / 225 \\
                 8.7 Affine Quadriken / 231 \\
                 8.8 Aufgaben / 241 \\
                 9 Ringe und Moduln / 244 \\
                 9.1 Ideale und Restklassenringe / 244 \\
                 9.2 Moduln / 248 \\
                 9.3 Kommutative Diagramme und exakte Folgen / 255 \\
                 9.4 Endlich erzeugte und freie Moduln / 257 \\
                 9.5 Matrizen und lineare Abbildungen freier Moduln /
                 262 \\
                 9.6 Direkte Produkte und lineare Abbildungen / 264 \\
                 9.7 Aufgaben / 276 \\
                 10 Multilineare Algebra / 279 \\
                 10.1 Multilineare Abbildungen und Tensorprodukte / 279
                 \\
                 10.2 Tensorprodukte von linearen Abbildungen / 287 \\
                 10.3 Ringerweiterungen und Tensorprodukte / 289 \\
                 10.4 {\"A}u{\ss}ere Potenzen und alternierende
                 Abbildungen / 292 \\
                 10.5 Determinante eines Endomorphismus / 298 \\
                 10.6 Aufgaben / 301 \\
                 11 Moduln {\"u}ber Hauptidealringen / 303 \\
                 11.1 Eindeutige Faktorzerlegung in Hauptidealringen /
                 304 \\
                 11.2 Torsionsmodul eines endlich erzeugten Moduls / 312
                 \\
                 11.3 Prim{\"a}rzerlegung / 315 \\
                 11.4 Struktursatz f{\"u}r endlich erzeugte Moduln / 318
                 \\
                 11.5 Elementarteiler von Matrizen / 324 \\
                 11.6 Aufgaben / 344 \\
                 12 Normalformen einer Matrix / 346 \\
                 12.1 Vektorr{\"a}ume als Moduln {\"u}ber einem
                 Polynomring / 346 \\
                 12.2 Rationale kanonische Form / 350 \\
                 12.3 Berechnungsverfahren f{\"u}r die Normalformen /
                 353 \\
                 12.4 Aufgaben / 365 \\
                 A Hinweise zur Benutzung von Computeralgebrasystemen /
                 367 \\
                 B L{\"o}sungen der Aufgaben / 372 \\
                 B.1 L{\"o}sungen zu Kapitel 1 / 372 \\
                 B.2 L{\"o}sungen zu Kapitel 2 / 373 \\
                 B.3 L{\"o}sungen zu Kapitel 3 / 374 \\
                 B.4 L{\"o}sungen zu Kapitel 4 / 378 \\
                 B.5 L{\"o}sungen zu Kapitel 5 / 380 \\
                 B.6 L{\"o}sungen zu Kapitel 6 / 382 \\
                 B.7 L{\"o}sungen zu Kapitel 7 / 388 \\
                 B.8 L{\"o}sungen zu Kapitel 8 / 391 \\
                 B.9 L{\"o}sungen zu Kapitel 9 / 395 \\
                 B.IO L{\"o}sungen zu Kapitel 10 / 397 \\
                 B.ll L{\"o}sungen zu Kapitel 11 / 399 \\
                 B.12 L{\"o}sungen zu Kapitel 12 / 402 \\
                 Literatur / 407 \\
                 Index / 409",
}

@Book{Kreyszig:1978:IFA,
  author =       "Erwin Kreyszig",
  title =        "Introductory Functional Analysis with Applications",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 688",
  year =         "1978",
  ISBN =         "0-471-50731-8 (hardcover), 0-471-50459-9 (paperback)",
  ISBN-13 =      "978-0-471-50731-4 (hardcover), 978-0-471-50459-7
                 (paperback)",
  LCCN =         "QA320 .K74",
  MRclass =      "46-01 (47-01)",
  MRnumber =     "0467220 (57 \#7084)",
  MRreviewer =   "T. A. Gillespie",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  URL =          "http://www.gbv.de/dms/bowker/toc/9780471504597.pdf;
                 http://www.zentralblattmath.org/zmath/en/search/?an=0706.46001",
  ZMnumber =     "0706.46001",
  abstract =     "Provides avenues for applying functional analysis to
                 the practical study of natural sciences as well as
                 mathematics. Contains worked problems on Hilbert space
                 theory and on Banach spaces and emphasizes concepts,
                 principles, methods and major applications of
                 functional analysis.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Metric Spaces \\
                 Normed Spaces \\
                 Banach Spaces \\
                 Inner Product Spaces \\
                 Hilbert Spaces \\
                 Fundamental Theorems for Normed and Banach Spaces \\
                 Further Applications: Banach Fixed Point Theorem \\
                 Spectral Theory of Linear Operators in Normed Spaces
                 \\
                 Compact Linear Operators on Normed Spaces and Their
                 Spectrum \\
                 Spectral Theory of Bounded Self-Adjoint Linear
                 Operators \\
                 Unbounded Linear Operators in Hilbert Space \\
                 Unbounded Linear Operators in Quantum Mechanics \\
                 Appendices \\
                 References \\
                 Index",
}

@Book{Lancaster:1969:TM,
  author =       "Peter Lancaster",
  title =        "Theory of Matrices",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xii + 316",
  year =         "1969",
  LCCN =         "QA263 .L33",
  MRclass =      "15.00",
  MRnumber =     "0245579 (39 \#6885)",
  MRreviewer =   "R. C. Thompson",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Lancaster:1985:TMA,
  author =       "Peter Lancaster and Miron Tismenetsky",
  title =        "The Theory of Matrices: with Applications",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  edition =      "Second",
  pages =        "xv + 570",
  year =         "1985",
  ISBN =         "0-12-435560-9",
  ISBN-13 =      "978-0-12-435560-6",
  LCCN =         "QA188 .L36 1985",
  MRclass =      "15-01 (15-02)",
  MRnumber =     "792300 (87a:15001)",
  MRreviewer =   "George P. Barker",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Computer Science and Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/description/els032/83015775.html;
                 http://www.loc.gov/catdir/toc/els031/83015775.html",
  abstract =     "In this book the authors try to bridge the gap between
                 the treatments of matrix theory and linear algebra. It
                 is aimed at graduate and advanced undergraduate
                 students seeking a foundation in mathematics, computer
                 science, or engineering. It will also be useful as a
                 reference book for those working on matrices and linear
                 algebra for use in their scientific work.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Matrix Algebra \\
                 Determinants, Inverse Matrices, and Rank \\
                 Linear, Euclidean, and Unitary Spaces \\
                 Linear Transformations and Matrices \\
                 Linear Transformations in Unitary Spaces and Simple
                 Matrices \\
                 The Jordan Canonical Form: A Geometric Approach \\
                 Matrix Polynomials and Normal Forms \\
                 The Variational Method \\
                 Functions of Matrices \\
                 Norms and Bounds for Eigenvalues \\
                 Perturbation Theory \\
                 Linear Matrix Equations and Generalized Inverses \\
                 Stability Problems \\
                 Matrix Polynomials \\
                 Nonnegative Matrices \\
                 Appendix 1 \\
                 A Survey of Scalar Polynomials \\
                 Appendix 2 \\
                 Some Theorems and Notions from Analysis \\
                 Appendix 3 \\
                 Suggestions for Further Reading \\
                 Index",
}

@Book{Lang:1987:LA,
  author =       "Serge Lang",
  title =        "Linear Algebra",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "x + 285",
  year =         "1987",
  DOI =          "https://doi.org/10.1007/978-1-4757-1949-9",
  ISBN =         "0-387-96412-6",
  ISBN-13 =      "978-0-387-96412-6",
  LCCN =         "QA251 .L26 1987",
  MRclass =      "15-01",
  MRnumber =     "874113 (88d:15001)",
  MRreviewer =   "S. Lajos",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Undergraduate Texts in Mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0814/86021943-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0814/86021943-t.html",
  abstract =     "\booktitle{Linear Algebra} is intended for a one-term
                 course at the junior or senior level. It begins with an
                 exposition of the basic theory of vector spaces and
                 proceeds to explain the fundamental structure theorem
                 for linear maps, including eigenvectors and
                 eigenvalues, quadratic and Hermitian forms,
                 diagonalization of symmetric, Hermitian, and unitary
                 linear maps and matrices, triangulation, and Jordan
                 canonical form. The book also includes a useful chapter
                 on convex sets and the finite-dimensional Krein-Milman
                 theorem. The presentation is aimed at the student who
                 has already had some exposure to the elementary theory
                 of matrices, determinants and linear maps. However the
                 book is logically self-contained. In this new edition,
                 many parts of the book have been rewritten and
                 reorganized, and new exercises have been added.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "1. Vector Spaces \\
                 2. Matrices \\
                 3. Linear Mappings \\
                 4. Linear Maps and Matrices \\
                 5. Scalar Products and Orthogonality \\
                 6. Determinants \\
                 7. Symmetric, Hermitian, and Unitary Operators \\
                 8. Eigenvectors and Eigenvalues \\
                 9. Polynomials and Matrices \\
                 10. Triangulation of Matrices and Linear Maps \\
                 11. Polynomials and Primary Decomposition \\
                 12. Convex Sets",
}

@Book{Lawson:1974:SLS,
  author =       "Charles L. Lawson and Richard J. Hanson",
  title =        "Solving Least Squares Problems",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 340",
  year =         "1974",
  ISBN =         "0-13-822585-0",
  ISBN-13 =      "978-0-13-822585-8",
  LCCN =         "QA275 .L38",
  MRclass =      "65F20",
  MRnumber =     "0366019 (51 \#2270)",
  MRreviewer =   "R. P. Tewarson",
  bibdate =      "Sun Nov 23 09:45:42 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Prentice-Hall Series in Automatic Computation",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Least squares; Data processing",
}

@Book{Lawson:1995:SLS,
  author =       "Charles L. Lawson and Richard J. Hanson",
  title =        "Solving Least Squares Problems",
  volume =       "15",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xii + 337",
  year =         "1995",
  ISBN =         "0-89871-356-0 (paperback)",
  ISBN-13 =      "978-0-89871-356-5 (paperback)",
  LCCN =         "QA275 .L38 1995",
  bibdate =      "Sun Nov 23 09:45:40 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Classics in applied mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0617/95035178-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0617/95035178-t.html",
  acknowledgement = ack-nhfb,
  remark =       "This SIAM edition is an unabridged, revised
                 republication of \cite{Lawson:1974:SLS}.",
  subject =      "Least squares; Data processing",
}

@Book{Lax:2007:LAA,
  author =       "Peter D. Lax",
  title =        "Linear Algebra and its Applications",
  publisher =    pub-WILEY-INTERSCIENCE,
  address =      pub-WILEY-INTERSCIENCE:adr,
  edition =      "Second",
  pages =        "xvi + 376",
  year =         "2007",
  ISBN =         "0-471-75156-1 (hardcover)",
  ISBN-13 =      "978-0-471-75156-4 (hardcover)",
  LCCN =         "QA184.2 .L38 2007",
  MRclass =      "15-01 (47-01)",
  MRnumber =     "2356919 (2008j:15002)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Pure and Applied Mathematics (Hoboken)",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0826/2007023226-b.html;
                 http://www.loc.gov/catdir/enhancements/fy0826/2007023226-d.html;
                 http://www.loc.gov/catdir/toc/ecip0719/2007023226.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Fundamentals \\
                 Duality \\
                 Linear mappings \\
                 Matrices \\
                 Determinant and trace \\
                 Spectral theory \\
                 Euclidean structure \\
                 Spectral theory of self-adjoint mappings \\
                 Calculus of vector- and matrix-valued functions \\
                 Matrix inequalities \\
                 Kinematics and dynamics \\
                 Convexity \\
                 The duality theorem \\
                 Normed linear spaces \\
                 Linear mappings between normed linear spaces \\
                 Positive matrices \\
                 How to solve systems of linear equations \\
                 How to calculate the eigenvalues of self-adjoint
                 matrices \\
                 Solutions",
}

@Book{Lay:1982:CST,
  author =       "Steven R. Lay",
  title =        "Convex Sets and Their Applications",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xvi + 244",
  year =         "1982",
  ISBN =         "0-471-09584-2",
  ISBN-13 =      "978-0-471-09584-2",
  ISSN =         "0079-8185",
  LCCN =         "QA640 .L38 1982",
  bibdate =      "Fri Nov 21 08:31:15 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Pure and applied mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "1944--",
  subject =      "Convex sets",
  tableofcontents = "1: Fundamentals / 1 \\
                 1. Linear Algebra and Topology / 1 \\
                 2. Convex Sets / 10 \\
                 2: Hyperplanes / 27 \\
                 3. Hyperplanes and Linear Functionals / 27 \\
                 4. Separating Hyperplanes / 33 \\
                 5. Supporting Hyperplanes / 41 \\
                 3: Helly-Type Theorems / 47 \\
                 6. Helly's Theorem / 47 \\
                 7. Kirchberger's Theorem / 55 \\
                 4: Kirchberger-type Theorems / 61 \\
                 8. Separation by a Spherical Surface / 61 \\
                 9. Separation by a Cylinder / 64 \\
                 10. Separation by a Parallelotope / 70 \\
                 5: Special Topics in $E^2$ / 76 \\
                 11. Sets of Constant Width / 76 \\
                 12. Universal Covers / 84 \\
                 13. The Isoperimetric Problem / 88 \\
                 6: Families of Convex Sets / 94 \\
                 14. Parallel Bodies / 94 \\
                 15. The Blaschke Selection Theorem / 97 \\
                 16. The Existence of Extremal Sets / 101 \\
                 7: Characterizations of Convex Sets / 104 \\
                 17. Local Convexity / 104 \\
                 18. Local Support Properties / 107 \\
                 19. Nearest-Point Properties / 111 \\
                 8: Polytopes / 116 \\
                 20. The Faces of a Polytope / 116 \\
                 21. Special Types of Polytopes and Euler's Formula /
                 123 \\
                 22. Approximation by Polytopes / 133 \\
                 9: Duality / 140 \\
                 23. Polarity and Polytopes / 140 \\
                 24. Dual Cones / 146 \\
                 10: Optimization / 154 \\
                 25. Finite Matrix Games / 154 \\
                 26. Linear Programming / 168 \\
                 27. The Simplex Method / 183 \\
                 11: Convex Functions / 198 \\
                 28. Basic Properties / 198 \\
                 29. Support and Distance Functions / 205 \\
                 30. Continuity and Differentiability / 214 \\
                 Solutions, Hints, and References for Exercises / 222
                 \\
                 Bibliography Index / 239",
}

@Book{Lay:1992:CST,
  author =       "Steven R. Lay",
  title =        "Convex Sets and Their Applications",
  publisher =    "Krieger Pub. Co.",
  address =      "Malabar, FL, USA",
  pages =        "xvi + 244",
  year =         "1992",
  ISBN =         "0-89464-537-4",
  ISBN-13 =      "978-0-89464-537-2",
  LCCN =         "QA640 .L38 1991",
  bibdate =      "Fri Nov 21 08:31:15 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1944--",
  remark =       "Reprint. Originally published: New York: Wiley,
                 1982.",
  subject =      "Convex sets",
  tableofcontents = "Fundamentals / 1 \\
                 Linear Algebra and Topology / 1 \\
                 Convex Sets / 10 \\
                 Hyperplanes / 27 \\
                 Hyperplanes and Linear Functionals / 27 \\
                 Separating Hyperplanes / 33 \\
                 Supporting Hyperplanes / 41 \\
                 Helly-Type Theorems / 47 \\
                 Helly's Theorem / 47 \\
                 Kirchberger's Theorem / 55 \\
                 Kirchberger-type Theorems / 61 \\
                 Separation by a Spherical Surface / 61 \\
                 Separation by a Cylinder / 64 \\
                 Separation by a Parallelotope / 70 \\
                 Special Topics in $E^2$ / 76 \\
                 Sets of Constant Width / 76 \\
                 Universal Covers / 84 \\
                 The Isoperimetric Problem / 88 \\
                 Families of Convex Sets / 94 \\
                 Parallel Bodies / 94 \\
                 The Blaschke Selection Theorem / 97 \\
                 The Existence of Extremal Sets / 101 \\
                 Characterizations of Convex Sets / 104 \\
                 Local Convexity / 104 \\
                 Local Support Properties / 107 \\
                 Nearest-Point Properties / 111 \\
                 Polytopes / 116 \\
                 The Faces of a Polytope / 116 \\
                 Special Types of Polytopes and Euler's Formula / 123
                 \\
                 Approximation by Polytopes / 133 \\
                 Duality / 140 \\
                 Polarity and Polytopes / 140 \\
                 Dual Cones / 146 \\
                 Optimization / 154 \\
                 Finite Matrix Games / 154 \\
                 Linear Programming / 168 \\
                 The Simplex Method / 183 \\
                 Convex Functions / 158 \\
                 Basic Properties / 198 \\
                 Support and Distance Functions / 205 \\
                 Continuity and Differentiability / 214 \\
                 Solutions, Hints, and References for Exercises / 222
                 \\
                 Bibliography / 234 \\
                 Index / 239",
}

@Book{Lay:2007:CST,
  author =       "Steven R. Lay",
  title =        "Convex Sets and Their Applications",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Dover",
  pages =        "xii + 244",
  year =         "2007",
  ISBN =         "0-486-45803-2 (paperback)",
  ISBN-13 =      "978-0-486-45803-8 (paperback)",
  LCCN =         "QA640 .L38 2007",
  bibdate =      "Fri Nov 21 08:31:15 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0707/2007000125-d.html",
  abstract =     "Suitable for advanced undergraduates and graduate
                 students, this text introduces the broad scope of
                 convexity. It leads students to open questions and
                 unsolved problems, and it highlights diverse
                 applications. Numerous examples, exercises, hints, and
                 answers appear throughout the text. The author is
                 Professor of Mathematics at Lee University in
                 Tennessee.",
  acknowledgement = ack-nhfb,
  author-dates = "1944--",
  remark =       "Originally published: New York: John Wiley and Sons,
                 1982.",
  subject =      "Convex sets",
}

@Book{MacDuffee:1933:TM,
  author =       "C. C. (Cyrus Colton) MacDuffee",
  title =        "The Theory of Matrices",
  volume =       "5",
  publisher =    "J. Springer",
  address =      "Berlin, Germany",
  pages =        "v + 110",
  year =         "1933",
  LCCN =         "QA263 .M32",
  bibdate =      "Fri Nov 21 09:42:14 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Ergebnisse der Mathematik und ihrer Grenzgebiete
                 \ldots{} 2",
  acknowledgement = ack-nhfb,
  author-dates = "1895--??",
}

@Book{MacDuffee:1946:TM,
  author =       "C. C. (Cyrus Colton) MacDuffee",
  title =        "The Theory of Matrices",
  publisher =    "Chelsea",
  address =      "New York, NY, USA",
  edition =      "Second",
  pages =        "v + 110",
  year =         "1946",
  LCCN =         "QA263 .M32",
  bibdate =      "Fri Nov 21 09:42:14 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1895--??",
}

@Book{MacDuffee:2004:TM,
  author =       "Cyrus Colton MacDuffee",
  title =        "The Theory of Matrices",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "x + 110",
  year =         "2004",
  ISBN =         "0-486-49590-6",
  ISBN-13 =      "978-0-486-49590-3",
  LCCN =         "QA188 .M33 2004",
  bibdate =      "Sun Nov 23 10:05:04 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Dover phoenix editions",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0617/2004045572-d.html",
  acknowledgement = ack-nhfb,
  author-dates = "1895--",
  remark =       "Originally published in \cite{MacDuffee:1946:TM}.",
  subject =      "Matrices",
}

@Book{Marcus:1964:SMT,
  author =       "Marvin Marcus and Henryk Minc",
  title =        "A Survey of Matrix Theory and Matrix Inequalities",
  publisher =    pub-ALLYN-BACON,
  address =      pub-ALLYN-BACON:adr,
  pages =        "xvi + 180",
  year =         "1964",
  LCCN =         "QA263 .M345",
  MRclass =      "15.00",
  MRnumber =     "0162808 (29 \#112)",
  MRreviewer =   "G. M. Petersen",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Marcus:1992:SMT,
  author =       "Marvin Marcus and Henryk Minc",
  title =        "A Survey of Matrix Theory and Matrix Inequalities",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xii + 180",
  year =         "1992",
  ISBN =         "0-486-67102-X (paperback)",
  ISBN-13 =      "978-0-486-67102-4 (paperback)",
  LCCN =         "QA188 .M36 1992",
  bibdate =      "Sun Nov 23 10:07:09 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/91039704.html",
  acknowledgement = ack-nhfb,
  author-dates = "1927--",
  remark =       "Originally published: Boston: Prindle, Weber and
                 Schmidt, 1964. (Prindle, Weber and Schmidt
                 Complementary Series in Mathematics, volume 14).",
  subject =      "Matrices; Matrix inequalities",
}

@Book{Marcus:1973:FDM,
  author =       "Marvin Marcus",
  title =        "Finite Dimensional Multilinear Algebra",
  volume =       "23(1)",
  publisher =    pub-DEKKER,
  address =      pub-DEKKER:adr,
  pages =        "x + 292",
  year =         "1973",
  ISBN =         "0-8247-6077-8 (vol. 1)",
  ISBN-13 =      "978-0-8247-6077-9 (vol. 1)",
  LCCN =         "QA184 .M37",
  bibdate =      "Fri Nov 21 11:14:50 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Pure and applied mathematics",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1927--",
  subject =      "Multilinear algebra",
}

@Book{Marcus:1975:FDM,
  author =       "Marvin Marcus",
  title =        "Finite Dimensional Multilinear Algebra",
  volume =       "23(2)",
  publisher =    pub-DEKKER,
  address =      pub-DEKKER:adr,
  pages =        "xvi + 718",
  year =         "1975",
  ISBN =         "0-8247-6203-7 (vol. 2)",
  ISBN-13 =      "978-0-8247-6203-2 (vol. 2)",
  LCCN =         "QA184 .M37",
  bibdate =      "Fri Nov 21 11:17:04 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Pure and applied mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "1927--",
}

@Book{Marshall:1979:ITM,
  author =       "Albert W. Marshall and Ingram Olkin",
  title =        "Inequalities: {Theory} of Majorization and Its
                 Applications",
  volume =       "143",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xx + 569",
  year =         "1979",
  ISBN =         "0-12-473750-1",
  ISBN-13 =      "978-0-12-473750-1",
  LCCN =         "QA295 .M42",
  MRclass =      "00A05 (05-02 15A42 15A45 52A40 60E15 65-02)",
  MRnumber =     "552278 (81b:00002)",
  MRreviewer =   "Michael O. Albertson",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Mathematics in Science and Engineering",
  URL =          "http://www.loc.gov/catdir/description/els031/79050218.html;
                 http://www.loc.gov/catdir/toc/els031/79050218.html",
  abstract =     "Although they play a fundamental role in nearly all
                 branches of mathematics, inequalities are usually
                 obtained by ad hoc methods rather than as consequences
                 of some underlying ``theory of inequalities.'' For
                 certain kinds of inequalities, the notion of
                 majorization leads to such a theory that is sometimes
                 extremely useful and powerful for deriving
                 inequalities. Moreover, the derivation of an inequality
                 by methods of majorization is often very helpful both
                 for providing a deeper understanding and for suggesting
                 natural generalizations.\par

                 Anyone wishing to employ majorization as a tool in
                 applications can make use of the theorems for the most
                 part, their statements are easily understood.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Theory of Majorization \\
                 Mathematical Applications \\
                 Stochastic Applications \\
                 Generalizations \\
                 Complementary Topics",
}

@Book{Marshall:2011:ITM,
  author =       "Albert W. Marshall and Ingram Olkin and Barry C.
                 Arnold",
  title =        "Inequalities: Theory of Majorization and Its
                 Applications",
  volume =       "??",
  publisher =    "Springer Science+Business Media, LLC",
  address =      "New York, NY, USA",
  edition =      "Second",
  pages =        "xxvii + 909",
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/978-0-387-68276-1",
  ISBN =         "0-387-40087-7, 0-387-68276-7 (e-book)",
  ISBN-13 =      "978-0-387-40087-7, 978-0-387-68276-1 (e-book)",
  ISSN =         "0172-7397",
  ISSN-L =       "0172-7397",
  LCCN =         "QA295 .M37 2011; QA295 .M42 2011",
  bibdate =      "Fri Nov 21 09:06:29 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/probstat2010.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Springer Series in Statistics",
  URL =          "http://link.springer.com/book/10.1007/978-0-387-68276-1;
                 http://www.loc.gov/catdir/enhancements/fy1114/2010931704-b.html;
                 http://www.loc.gov/catdir/enhancements/fy1114/2010931704-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1114/2010931704-t.html",
  abstract =     "Statisticians, probabilists, and mathematicians will
                 all be interested in a expanded version of this classic
                 work on inequalities. The theory of inequalities has
                 applications in virtually every branch of
                 mathematics.",
  acknowledgement = ack-nhfb,
  remark =       "Most volumes in this series are unnumbered.",
  series-URL =   "http://link.springer.com/bookseries/692",
  subject =      "Inequalities (Mathematics); Mathematics; MATHEMATICS /
                 Infinity; Inequalities (Mathematics)",
  tableofcontents = "I Theory of Majorization \\
                 1 Introduction / 3 \\
                 A Motivation and Basic Definitions / 3 \\
                 B Majorization as a Partial Ordering / 18 \\
                 C Order-Preserving Functions / 19 \\
                 D Various Generalizations of Majorization / 21 \\
                 2 Doubly Stochastic Matrices / 29 \\
                 A Doubly Stochastic Matrices and Permutation Matrices /
                 29 \\
                 B Characterization of Majorization Using Doubly
                 Stochastic Matrices / 32 \\
                 C Doubly Substochastic Matrices and Weak Majorization /
                 36 \\
                 D Doubly Superstochastic Matrices and Weak Majorization
                 / 42 \\
                 E Orderings on $\cal D$ / 45 \\
                 F Proofs of Birkhoff's Theorem and Refinements / 47 \\
                 G Classes of Doubly Stochastic Matrices / 52 \\
                 H More Examples of Doubly Stochastic and Doubly
                 Substochastic Matrices / 61 \\
                 I Properties of Doubly Stochastic Matrices / 67 \\
                 J Diagonal Equivalence of Nonnegative Matrices / 76 \\
                 3 Schur-Convex Functions / 79 \\
                 A Characterization of Schur-Convex Functions / 80 \\
                 B Compositions Involving Schur-Convex Functions / 88
                 \\
                 C Some General Classes of Schur-Convex Functions / 91
                 \\
                 D Examples I. Sums of Convex Functions / 101 \\
                 E Examples II. Products of Logarithmically Concave
                 (Convex) Functions / 105 \\
                 F Examples III. Elementary Symmetric Functions / 114
                 \\
                 G Muirhead's Theorem / 120 \\
                 H Schur-Convex Functions on $\cal D$ and Their
                 Extension to ${\cal R}^n$ / 132 \\
                 I Miscellaneous Specific Examples / 138 \\
                 J Integral Transformations Preserving Schur-Convexity /
                 145 \\
                 K Physical Interpretations of Inequalities / 153 \\
                 4 Equivalent Conditions for Majorization / 155 \\
                 A Characterization by Linear Transformations / 155 \\
                 B Characterization in Terms of Order-Preserving
                 Functions / 156 \\
                 C A Geometric Characterization / 162 \\
                 D A Characterization Involving Top Wage Earners / 163
                 \\
                 5 Preservation and Generation of Majorization / 165 \\
                 A Operations Preserving Majorization / 165 \\
                 B Generation of Majorization / 185 \\
                 C Maximal and Minimal Vectors Under Constraints / 192
                 \\
                 D Majorization in Integers / 194 \\
                 E Partitions / 199 \\
                 F Linear Transformations That Preserve Majorization /
                 202 \\
                 6 Rearrangements and Majorization / 203 \\
                 A Majorizations from Additions of Vectors / 204 \\
                 B Majorizations from Functions of Vectors / 210 \\
                 C Weak Majorizations from Rearrangements / 213 \\
                 D $L$-Superadditive Functions --- Properties and
                 Examples / 217 \\
                 E Inequalities Without Majorization / 225 \\
                 F A Relative Arrangement Partial Order / 228 \\
                 II Mathematical Applications \\
                 7 Combinatorial Analysis / 243 \\
                 A Some Preliminaries on Graphs, Incidence Matrices, and
                 Networks / 243 \\
                 B Conjugate Sequences / 245 \\
                 C The Theorem of Gale and Ryser / 249 \\
                 D Some Applications of the Gale--Ryser Theorem / 254
                 \\
                 E $s$-Graphs and a Generalization of the Gale--Ryser
                 Theorem / 258 \\
                 F Tournaments / 260 \\
                 G Edge Coloring in Graphs / 265 \\
                 H Some Graph Theory Settings in Which Majorization
                 Plays a Role / 267 \\
                 8 Geometric Inequalities / 269 \\
                 A Inequalities for the Angles of a Triangle / 271 \\
                 B Inequalities for the Sides of a Triangle / 276 \\
                 C Inequalities for the Exradii and Altitudes / 282 \\
                 D Inequalities for the Sides, Exradii, and Medians /
                 284 \\
                 E Isoperimetric-Type Inequalities for Plane Figures /
                 287 \\
                 F Duality Between Triangle Inequalities and
                 Inequalities Involving Positive Numbers / 294 \\
                 G Inequalities for Polygons and Simplexes / 295 \\
                 9 Matrix Theory / 297 \\
                 A Notation and Preliminaries / 298 \\
                 B Diagonal Elements and Eigenvalues of a Hermitian
                 Matrix / 300 \\
                 C Eigenvalues of a Hermitian Matrix and Its Principal
                 Submatrices / 308 \\
                 D Diagonal Elements and Singular Values / 313 \\
                 E Absolute Value of Eigenvalues and Singular Values /
                 317 \\
                 F Eigenvalues and Singular Values / 324 \\
                 G Eigenvalues and Singular Values of $A$, $B$, and $A +
                 B$ / 329 \\
                 H Eigenvalues and Singular Values of $A$, $B$, and $A
                 B$ / 338 \\
                 I Absolute Values of Eigenvalues and Row Sums / 347 \\
                 J Schur or Hadamard Products of Matrices / 352 \\
                 K A Totally Positive Matrix and an $M$-Matrix / 357 \\
                 L L{\"o}wner Ordering and Majorization / 360 \\
                 M Nonnegative Matrix-Valued Functions / 361 \\
                 N Zeros of Polynomials / 362 \\
                 O Other Settings in Matrix Theory Where Majorization
                 Has Proved Useful / 363 \\
                 10 Numerical Analysis / 367 \\
                 A Unitarily Invariant Norms and Symmetric Gauge
                 Functions / 367 \\
                 B Matrices Closest to a Given Matrix / 370 \\
                 C Condition Numbers and Linear Equations / 376 \\
                 D Condition Numbers of Submatrices and Augmented
                 Matrices / 380 \\
                 E Condition Numbers and Norms / 380 \\
                 III Stochastic Applications \\
                 11 Stochastic Majorizations / 387 \\
                 A Introduction / 387 \\
                 B Convex Functions and Exchangeable Random Variables /
                 392 \\
                 C Families of Distributions Parameterized to Preserve
                 Symmetry and Convexity / 397 \\
                 D Some Consequences of the Stochastic Majorization
                 $E_1(P_1)$ / 401 \\
                 E Parameterization to Preserve Schur-Convexity / 403
                 \\
                 F Additional Stochastic Majorizations and Properties /
                 420 \\
                 G Weak Stochastic Majorizations / 427 \\
                 H Additional Stochastic Weak Majorizations and
                 Properties / 435 \\
                 I Stochastic Schur-Convexity / 440 \\
                 12 Probabilistic, Statistical, and Other Applications /
                 441 \\
                 A Sampling from a Finite Population / 442 \\
                 B Majorization Using Jensen's Inequality / 456 \\
                 C Probabilities of Realizing at Least $k$ of $n$ Events
                 / 457 \\
                 D Expected Values of Ordered Random Variables / 461 \\
                 E Eigenvalues of a Random Matrix / 469 \\
                 F Special Results for Bernoulli and Geometric Random
                 Variables / 474 \\
                 G Weighted Sums of Symmetric Random Variables / 476 \\
                 H Stochastic Ordering from Ordered Random Variables /
                 481 \\
                 I Another Stochastic Majorization Based on Stochastic
                 Ordering / 487 \\
                 J Peakedness of Distributions of Linear Combinations /
                 490 \\
                 K Tail Probabilities for Linear Combinations / 494 \\
                 L Schur-Concave Distribution Functions and Survival
                 Functions / 500 \\
                 M Bivariate Probability Distributions with Fixed
                 Marginals / 505 \\
                 N Combining Random Variables / 507 \\
                 O Concentration Inequalities for Multivariate
                 Distributions / 510 \\
                 P Miscellaneous Cameo Appearances of Majorization / 511
                 \\
                 Q Some Other Settings in Which Majorization Plays a
                 Role / 525 \\
                 13 Additional Statistical Applications / 527 \\
                 A Unbiasedness of Tests and Monotonicity of Power
                 Functions / 528 \\
                 B Linear Combinations of Observations / 535 \\
                 C Ranking and Selection / 541 \\
                 D Majorization in Reliability Theory / 549 \\
                 E Entropy / 556 \\
                 F Measuring Inequality and Diversity / 559 \\
                 G Schur-Convex Likelihood Functions / 566 \\
                 H Probability Content of Geometric Regions for
                 Schur-Concave Densities / 567 \\
                 I Optimal Experimental Design / 568 \\
                 J Comparison of Experiments / 570 \\
                 IV Generalizations \\
                 14 Orderings Extending Majorization / 577 \\
                 A Majorization with Weights / 578 \\
                 B Majorization Relative to $d$ / 585 \\
                 C Semigroup and Group Majorization / 587 \\
                 D Partial Orderings Induced by Convex Cones / 595 \\
                 E Orderings Derived from Function Sets / 598 \\
                 F Other Relatives of Majorization / 603 \\
                 G Majorization with Respect to a Partial Order / 605
                 \\
                 H Rearrangements and Majorizations for Functions / 606
                 \\
                 15 Multivariate Majorization / 611 \\
                 A Some Basic Orders / 611 \\
                 B The Order-Preserving Functions / 621 \\
                 C Majorization for Matrices of Differing Dimensions /
                 623 \\
                 D Additional Extensions / 628 \\
                 E Probability Inequalities / 630 \\
                 V Complementary Topics \\
                 16 Convex Functions and Some Classical Inequalities /
                 637 \\
                 A Monotone Functions / 637 \\
                 B Convex Functions / 641 \\
                 C Jensen's Inequality / 654 \\
                 D Some Additional Fundamental Inequalities / 657 \\
                 E Matrix-Monotone and Matrix-Convex Functions / 670 \\
                 F Real-Valued Functions of Matrices / 684 \\
                 17 Stochastic Ordering / 693 \\
                 A Some Basic Stochastic Orders / 694 \\
                 B Stochastic Orders from Convex Cones / 700 \\
                 C The Lorenz Order / 712 \\
                 D Lorenz Order: Applications and Related Results / 734
                 \\
                 E An Uncertainty Order / 748 \\
                 18 Total Positivity / 757 \\
                 A Totally Positive Functions / 757 \\
                 B P{\'o}lya Frequency Functions / 762 \\
                 C P{\'o}lya Frequency Sequences / 767 \\
                 D Total Positivity of Matrices / 767 \\
                 19 Matrix Factorizations, Compounds, Direct Products,
                 and $M$-Matrices / 769 \\
                 A Eigenvalue Decompositions / 769 \\
                 B Singular Value Decomposition / 771 \\
                 C Square Roots and the Polar Decomposition / 772 \\
                 D A Duality Between Positive Semidefinite Hermitian
                 Matrices / 774 \\
                 E Simultaneous Reduction of Two Hermitian Matrices /
                 775 \\
                 F Compound Matrices / 775 \\
                 G Kronecker Product and Sum / 780 \\
                 H $M$-Matrices / 782 \\
                 20 Extremal Representations of Matrix Functions / 783
                 \\
                 A Eigenvalues of a Hermitian Matrix / 783 \\
                 B Singular Values / 789 \\
                 C Other Extremal Representations / 794 \\
                 Erratum E1 \\
                 Biographies / 797 \\
                 References / 813 \\
                 Author Index / 879 \\
                 Subject Index / 893",
}

@Book{Minc:1988:NM,
  author =       "Henryk Minc",
  title =        "Nonnegative Matrices",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 206",
  year =         "1988",
  ISBN =         "0-471-83966-3",
  ISBN-13 =      "978-0-471-83966-8",
  LCCN =         "QA188 .M558 1988",
  MRclass =      "15-02 (15A48)",
  MRnumber =     "932967 (89i:15001)",
  MRreviewer =   "Thomas L. Markham",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Wiley-Interscience Series in Discrete Mathematics and
                 Optimization",
  URL =          "http://www.loc.gov/catdir/description/wiley034/87027416.html;
                 http://www.loc.gov/catdir/toc/onix05/87027416.html",
  abstract =     "This text\slash reference is the most up-to-date
                 volume on nonnegative matrices in print and presents
                 much material that was previously available only in
                 research papers. It is the only book to cover the van
                 der Waerden conjecture on permanents. There is also
                 coverage of doubly stochastic matrices and inverse
                 problems. The material has abundant connections to
                 graph theory, incidence geometry, stochastic processes,
                 functional analysis, and quadratic forms. Each chapter
                 contains a comprehensive set of problems and a
                 substantial list of references.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Spectral Properties of Nonnegative Matrices \\
                 Localization of the Maximal Eigenvalue \\
                 Primitive and Imprimitive Matrices \\
                 Structural Properties of Nonnegative Matrices \\
                 Doubly Stochastic Matrices \\
                 Other Types of Nonnegative Matrices \\
                 Inverse Eigenvalue Problems \\
                 Index",
}

@Book{Mirsky:1955:ILA,
  author =       "Leonid Mirsky",
  title =        "An Introduction to Linear Algebra",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xi + 433",
  year =         "1955",
  LCCN =         "QA251 .M5",
  MRclass =      "15.0X",
  MRnumber =     "0074364 (17,573a)",
  MRreviewer =   "M. F. Smiley",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
}

@Book{Mirsky:1961:ILA,
  author =       "Leonid Mirsky",
  title =        "An Introduction to Linear Algebra",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xi + 440",
  year =         "1961",
  LCCN =         "QA251 .M5",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Reprinted in \cite{Mirsky:1990:ILA}.",
  xxpages =      "viii + 440",
}

@Book{Mirsky:1963:ILA,
  author =       "Leonid Mirsky",
  title =        "An Introduction to Linear Algebra",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xi + 433",
  year =         "1963",
  LCCN =         "????",
  MRclass =      "15.0X",
  MRnumber =     "0074364 (17,573a)",
  MRreviewer =   "M. F. Smiley",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Mirsky:1982:ILA,
  author =       "Leonid Mirsky",
  title =        "An Introduction to Linear Algebra",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 433",
  year =         "1982",
  ISBN =         "0-486-61547-2",
  ISBN-13 =      "978-0-486-61547-9",
  LCCN =         "QA184 .M57 1982",
  bibdate =      "Fri Nov 21 11:25:09 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover033/90040299.html",
  acknowledgement = ack-nhfb,
  remark =       "Reprint of \cite{Mirsky:1955:ILA}.",
  subject =      "Algebras, Linear",
}

@Book{Mirsky:1990:ILA,
  author =       "Leonid Mirsky",
  title =        "An Introduction to Linear Algebra",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "viii + 440",
  year =         "1990",
  ISBN =         "0-486-66434-1 (paperback)",
  ISBN-13 =      "978-0-486-66434-7 (paperback)",
  LCCN =         "QA184 .M57 1990",
  bibdate =      "Fri Nov 21 11:25:09 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover033/90040299.html;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0766.15001",
  ZMnumber =     "0766.15001",
  abstract =     "Rigorous, self-contained coverage of determinants,
                 vectors, matrices and linear equations, quadratic
                 forms, more. Elementary, easily readable account with
                 numerous examples and problems at the end of each
                 chapter.",
  acknowledgement = ack-nhfb,
  remark =       "Reprint of \cite{Mirsky:1955:ILA}.",
  subject =      "Algebras, Linear",
}

@Book{Muir:1906:TDH,
  author =       "{Sir} Thomas Muir",
  title =        "The Theory of Determinants in the Historical Order of
                 Development",
  publisher =    pub-MACMILLAN,
  address =      pub-MACMILLAN:adr,
  pages =        "xii + 491 (vol. 1), xvi + 475 (vol. 2), xxvi + 503
                 (vol. 3), xxxi + 508 (vol. 4)",
  year =         "1906, 1911, 1920, 1923",
  LCCN =         "QA191 .M9",
  bibdate =      "Fri Nov 21 11:29:49 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Four volumes.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1844--1934",
  subject =      "Determinants",
  tableofcontents = "Vol. 1, Part 1: General determinants up to 1841 \\
                 Vol. 1, Part 2: Special determinants up to 1841 \\
                 Vol. 2: The Period 1841 to 1860 \\
                 Vol. 3: The Period 1861 to 1880 \\
                 Vol. 4: The Period 1880 to 1900",
}

@Book{Muir:1930:CHD,
  author =       "{Sir} Thomas Muir",
  title =        "Contributions to the History of Determinants,
                 1900--1920",
  publisher =    "Blackie and Son",
  address =      "London and Glasgow, UK",
  pages =        "xxiii + 1 + 408",
  year =         "1930",
  LCCN =         "QA191 .M88",
  bibdate =      "Fri Nov 21 11:41:39 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1844--1934",
  subject =      "Determinants",
}

@Book{Muir:1960:TDH,
  author =       "{Sir} Thomas Muir",
  title =        "The Theory of Determinants in the Historical Order of
                 Development",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "????",
  year =         "1960",
  LCCN =         "QA191 .M92",
  bibdate =      "Fri Nov 21 11:29:49 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "4 original volumes in 2 reprint volumes.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1844--1934",
  subject =      "Determinants",
}

@Book{Muir:1960:TTD,
  author =       "{Sir} Thomas Muir",
  title =        "A Treatise on the Theory of Determinants",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "766",
  year =         "1960",
  LCCN =         "QA191 .M85 1960",
  bibdate =      "Fri Jul 22 08:34:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Corrected printing of the 1933 edition, revised and
                 enlarged by William H. Metzler.",
  acknowledgement = ack-nhfb,
  author-dates = "1844--1934",
}

@Book{Newman:1972:IM,
  author =       "Morris Newman",
  title =        "Integral Matrices",
  volume =       "45",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 224",
  year =         "1972",
  ISBN =         "0-12-517850-6",
  ISBN-13 =      "978-0-12-517850-1",
  LCCN =         "QA3 .P8 1972",
  MRclass =      "15A33",
  MRnumber =     "0340283 (49 \#5038)",
  MRreviewer =   "B. M. Stewart",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Pure and Applied Mathematics",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface \\
                 Acknowledgments \\
                 I. Background Material on Rings \\
                 1. Principal Ideal Rings \\
                 2. Units \\
                 3. Divisibility \\
                 4. Congruence and Norms \\
                 5. The Ascending Chain Condition \\
                 6. Unique Factorization \\
                 7. Euclidean Rings \\
                 8. The Chinese Remainder Theorem \\
                 Exercises and Problems \\
                 II. Equivalence \\
                 1. Definition of Matrix Ring $S_n$, over $S$ \\
                 2. Units of $S_n$ \\
                 3. Definition of Equivalence \\
                 4. Elementary Row Operations \\
                 5. Completion to a Unimodular Matrix \\
                 6. The Hermite Normal Form \\
                 7. Divisor Sums \\
                 8. The Hermite Normal Form Class Number \\
                 9. An Application of the Hermite Normal Form \\
                 10. Left Equivalence over a Euclidean Ring \\
                 11. Generators of $R_n'$ when $R$ is Euclidean \\
                 12. Two-sided Equivalence \\
                 13. Determinantal Divisors \\
                 14. Multiples \\
                 15. The Smith Normal Form \\
                 16. Invariant Factors \\
                 17. Elementary Divisors \\
                 18. Divisibility Properties of the Invariant Factors
                 \\
                 19. The Multiplicativity of the Smith Normal Form \\
                 20. The Smith Normal Form Class Number \\
                 21. Applications of the Smith Normal Form \\
                 Exercises and Problems \\
                 III. Similarity \\
                 1. Definition of Similarity \\
                 2. A General Result for Any Principal Ideal Ring \\
                 3. Similarity over a Field \\
                 4. Degree and Proper Degree \\
                 5. A Modified Euclidean Algorithm \\
                 6. Two Lemmas on Degree and Proper Degree \\
                 7. The Fundamental Theorem on Similarity over a Field
                 \\
                 8. Minimal Polynomials and Nonderogatory Matrices \\
                 9. Companion Matrices \\
                 10. The Frobenius Normal Form \\
                 11. Jordan Matrices \\
                 12. The Jordan Normal Form \\
                 13. Criteria for Similarity to a Diagonal Matrix \\
                 14. Similarity over $\mathbb{Z}$ \\
                 15. Similarity to a Block Triangular Matrix \\
                 16. The Theorem of Latimer and MacDuffee \\
                 Exercises and Problems \\
                 IV. Congruence \\
                 1. Definition of Congruence \\
                 2. Definition of Quadratic Form \\
                 3. The Skew Normal Form \\
                 4. A General Result for Symmetric Matrices \\
                 5. The Connection between Symmetric Matrices and
                 Quadratic Forms \\
                 6. The Set $q(A)$ \\
                 7. Results on Elements Represented by Forms \\
                 8. Congruence over a Field \\
                 9. Congruence over a Field of Characteristic $2$ \\
                 10. Congruence over an Algebraically Closed Field of
                 Characteristic $2$ \\
                 11. Witt's Theorem \\
                 12. Two Lemmas on Finite Fields \\
                 13. Congruence over a Field of Finite Characteristic
                 \\
                 14. Two Lemmas on Finite Fields of Characteristic $2$
                 \\
                 15. Congruence over Finite Fields of Characteristic $2$
                 \\
                 16. Ordered Fields \\
                 17. Sylvester's Law of Inertia \\
                 18. Congruence over the Real Field \\
                 19. Positive Definite Matrices \\
                 20. Congruence over the Rational Field \\
                 21. Congruence over $\mathbb{Z}$ \\
                 22. The Arithmetic Minimum \\
                 23. The Case $n = 2$ \\
                 24. The Finiteness of the Class Number for $n = 2$ \\
                 25. The General Case: Hermite's Method \\
                 26. The Finiteness of the Class Number for Any $n$ \\
                 Exercises and Problems \\
                 V. Combined Similarity and Congruence \\
                 1. Orthogonal Equivalence \\
                 2. Orthogonal Equivalence over a Field of
                 Characteristic is not equal to $2$ \\
                 3. A Lemma of Hall and Ryser",
}

@Book{Noble:1969:ALA,
  author =       "Ben Noble and James W. Daniel",
  title =        "Applied Linear Algebra",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xvi + 523",
  year =         "1969",
  LCCN =         "QA184 .N6 1969",
  MRclass =      "15-01",
  MRnumber =     "0572995 (58 \#28016)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
}

@Book{Noble:1977:ALA,
  author =       "Ben Noble and James W. Daniel",
  title =        "Applied Linear Algebra",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  edition =      "Second",
  pages =        "xvii + 477",
  year =         "1977",
  ISBN =         "0-13-041343-7",
  ISBN-13 =      "978-0-13-041343-7",
  LCCN =         "QA184 .N6 1977",
  MRclass =      "15-01",
  MRnumber =     "0572995 (58 \#28016)",
  bibdate =      "Sun Nov 23 10:33:17 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Algebras, Linear",
}

@Book{Noble:1988:ALA,
  author =       "Ben Noble and James W. Daniel",
  title =        "Applied Linear Algebra",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  edition =      "Third",
  pages =        "xvi + 521",
  year =         "1988",
  ISBN =         "0-13-041260-0, 0-13-040957-X (paperback)",
  ISBN-13 =      "978-0-13-041260-7, 978-0-13-040957-7 (paperback)",
  LCCN =         "QA184 .N61 1988",
  MRclass =      "15-01",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "http://www.gbv.de/dms/bowker/toc/9780130412607.pdf",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Matrix Algebra \\
                 Some Simple Applications and Questions \\
                 Solving Equations and Finding Inverses: Methods \\
                 Solving Equations and Finding Inverses: Theory \\
                 Vectors and Vector Spaces \\
                 Introduction; Geometrical Vectors \\
                 Linear Transformations and Matrices \\
                 Eigenvalues and Eigenvectors: An Overview \\
                 Eigensystems of Symmetric Hermitian, and Normal
                 Matrices, with Applications \\
                 Eigensystems of General Matrices, with Applications \\
                 Quadratic Forms and Variational Characterizations of
                 Eigenvalues \\
                 Linear Programming \\
                 Answers and Aids to Selected Problems \\
                 Bibliography \\
                 Index",
}

@Book{Noble:1989:ALA,
  author =       "Ben Noble and James W. Daniel and Virgilio
                 {Gonz{\'a}lez Pozo}",
  title =        "Algebra lineal aplicada",
  publisher =    "Prentice Hall Hispanoamericana",
  address =      "M{\'e}xico, DF, M{\'e}xico",
  pages =        "xvii + 572",
  year =         "1989",
  ISBN =         "968-880-173-9, 0-13-041260-0",
  ISBN-13 =      "978-968-880-173-4, 978-0-13-041260-7",
  LCCN =         "QA184 .N618 1989",
  bibdate =      "Sat Nov 22 07:58:27 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  remark =       "Spanish translation of \cite{Noble:1988:ALA}.",
  subject =      "Algebras, Linear; Algebra lineal; Algebras, Linear.",
}

@Book{OMeara:2011:ATL,
  author =       "Kevin C. O'Meara and John Clark and Charles I.
                 Vinsonhaler",
  title =        "Advanced Topics in Linear Algebra: Weaving Matrix
                 Problems Through the {Weyr Form}",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xxii + 400",
  year =         "2011",
  ISBN =         "0-19-979373-5 (hardcover)",
  ISBN-13 =      "978-0-19-979373-0 (hardcover)",
  LCCN =         "QA184.2 .O44 2011",
  MRclass =      "15-02 (15A21 15A30)",
  MRnumber =     "2849857",
  MRreviewer =   "Huajun Huang",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Algebras, Linear",
  tableofcontents = "Background linear algebra \\
                 The Weyr form \\
                 Centralizers \\
                 The module setting \\
                 Gerstenhaber's theorem \\
                 Approximate simultaneous diagonalization \\
                 Algebraic varieties",
}

@Book{Ortega:1987:MTS,
  author =       "James McDonough Ortega",
  title =        "Matrix Theory: a Second Course",
  publisher =    pub-PLENUM,
  address =      pub-PLENUM:adr,
  pages =        "xii + 262",
  year =         "1987",
  DOI =          "https://doi.org/10.1007/978-1-4899-0471-3",
  ISBN =         "0-306-42433-9, 1-4899-0471-9 (e-book)",
  ISBN-13 =      "978-0-306-42433-5, 978-1-4899-0471-3 (e-book)",
  LCCN =         "QA188 .O78 1987",
  MRclass =      "15-01",
  MRnumber =     "878977 (88a:15002)",
  MRreviewer =   "George P. Barker",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "The University Series in Mathematics",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002910694.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0654.15001",
  ZMnumber =     "0654.15001",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "1. Review of Basic Background / 1 \\
                 1.1. Matrices and Vectors / 1 \\
                 1.2. Determinants / 11 \\
                 1.3. Linear Equations and Inverses / 15 \\
                 1.4. Eigenvalues and Eigenvectors / 29 \\
                 2. Linear Spaces and Operators / 43 \\
                 2.1. Linear Spaces / 43 \\
                 2.2. Linear Operators / 51 \\
                 2.3. Linear Equations, Rank, Inverses, and Eigenvalues
                 / 60 \\
                 2.4. Inner Product Spaces / 73 \\
                 2.5. Normed Linear Spaces / 90 \\
                 3. Canonical Forms / 105 \\
                 3.1. Orthogonal and Unitary Similarity Transformations
                 / 106 \\
                 3.2. The Jordan Canonical Form / 117 \\
                 3.3. Equivalence Transformations / 131 \\
                 4. Quadratic Forms and Optimization / 143 \\
                 4.1. The Geometry of Quadratic Forms / 143 \\
                 4.2. Optimization Problems / 151 \\
                 4.3. Least Squares Problems and Generalized Inverses /
                 158 \\
                 5. Differential and Difference Equations / 175 \\
                 5.1. Differential Equations and Matrix Exponentials /
                 175 \\
                 5.2. Stability / 189 \\
                 5.3. Difference Equations and Iterative Methods / 195
                 \\
                 5.4. Lyapunov's Theorem and Related Results / 203 \\
                 6. Other Topics / 215 \\
                 6.1. Nonnegative Matrices and Related Results / 215 \\
                 6.2. Generalized and Higher-Order Eigenvalue Problems /
                 230 \\
                 6.3. Some Special Matrices / 236 \\
                 6.4. Matrix Equations / 246 \\
                 References / 257 \\
                 Index / 259",
}

@Book{Parlett:1980:SEP,
  author =       "Beresford N. Parlett",
  title =        "The Symmetric Eigenvalue Problem",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xix + 348",
  year =         "1980",
  ISBN =         "0-13-880047-2",
  ISBN-13 =      "978-0-13-880047-5",
  LCCN =         "QA188 .P3",
  MRclass =      "65F15 (15A18)",
  MRnumber =     "MR570116 (81j:65063)",
  MRreviewer =   "Robert Todd Gregory",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/all_brec.bib;
                 https://www.math.utah.edu/pub/tex/bib/gvl.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Prentice-Hall Series in Computational Mathematics",
  series =       "Series in Computational Mathematics",
  ZMnumber =     "0431.65017",
  acknowledgement = ack-nhfb,
  classmath =    "65F15 Eigenvalues (numerical linear algebra) 15A18
                 Eigenvalues of matrices, etc. 15A57 Other types of
                 matrices 15-02 Research monographs (linear algebra)
                 65-02 Research monographs (numerical analysis) 15A23
                 Factorization of matrices 65F25 Orthogonalization
                 (numerical linear algebra)",
  keywords =     "bandmatrices; bounds for eigenvalues; eigenvalues;
                 generalized eigenvalue problem; Krylov sequences;
                 localization of eigenvalues; orthogonal
                 transformations; tridiagonal matrices; vector
                 iteration",
}

@Book{Parlett:1998:SEP,
  author =       "Beresford N. Parlett",
  title =        "The Symmetric Eigenvalue Problem",
  volume =       "20",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxiv + 398",
  year =         "1998",
  DOI =          "https://doi.org/10.1137/1.9781611971163",
  ISBN =         "0-89871-402-8 (paperback), 1-61197-116-0 (e-book)",
  ISBN-13 =      "978-0-89871-402-9 (paperback), 978-1-61197-116-3
                 (e-book)",
  LCCN =         "QA188 .P37 1998",
  MRclass =      "65F15 (15A18)",
  MRnumber =     "MR1490034 (99c:65072)",
  MRreviewer =   "F. Szidarovszky",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Corrected reprint \cite{Parlett:1980:SEP}.",
  series =       "Classics in Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0708/97040623-d.html",
  ZMnumber =     "0885.65039",
  abstract =     "According to Parlett, ``Vibrations are everywhere, and
                 so too are the eigenvalues associated with them. As
                 mathematical models invade more and more disciplines,
                 we can anticipate a demand for eigenvalue calculations
                 in an ever richer variety of contexts''. Anyone who
                 performs these calculations will welcome the reprinting
                 of Parlett's book (originally published in 1980). In
                 this unabridged, amended version, Parlett covers
                 aspects of the problem that are not easily found
                 elsewhere. The chapter titles convey the scope of the
                 material succinctly. The aim of the book is to present
                 mathematical knowledge that is needed in order to
                 understand the art of computing eigenvalues of real
                 symmetric matrices, either all of them or only a few.
                 The author explains why the selected information really
                 matters and he is not shy about making judgments. The
                 commentary is lively but the proofs are terse. The
                 first nine chapters are based on a matrix on which it
                 is possible to make similarity transformations
                 explicitly. The only source of error is inexact
                 arithmetic. The last five chapters turn to large sparse
                 matrices and the task of making approximations and
                 judging them.",
  acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah # "
                 and " # ack-crj,
  classmath =    "65F15 Eigenvalues (numerical linear algebra) 15A18
                 Eigenvalues of matrices, etc. 15A23 Factorization of
                 matrices 15A57 Other types of matrices 15-02 Research
                 monographs (linear algebra) 65-02 Research monographs
                 (numerical analysis) 65F25 Orthogonalization (numerical
                 linear algebra)",
  keywords =     "bandmatrices; bounds for eigenvalues; eigenvalues;
                 generalized eigenvalue problem; Krylov sequences;
                 localization of eigenvalues; orthogonal
                 transformations; tridiagonal matrices; vector
                 iteration",
  libnote =      "Not yet in my library.",
  remark =       "Unabridged, corrected republication of the original
                 edition (1980)",
  subject =      "Convergence theory for the Rayleigh quotient
                 iteration; Eigenvectors of tridiagonals; Convergence
                 theory, simpler than Wilkinson's, for Wilkinson's shift
                 strategy in $ Q L $ and $ Q R $; New proofs and sharper
                 results for error bounds; Optimal properties of
                 Rayleigh--Ritz approximations; Approximation theory
                 from Krylov subspaces, Paige's theorem for noisy
                 Lanczos algorithms, and semiorthogonality among Lanczos
                 vectors; Four flavors of subspace iteration",
  tableofcontents = "Front Matter / i--xxvi \\
                 1. Basic Facts about Self-Adjoint Matrices / 1--19 \\
                 2. Tasks, Obstacles, and Aids / 21--42 \\
                 3. Counting Eigenvalues / 43--60 \\
                 4. Simple Vector Iterations / 61--85 \\
                 5. Deflation / 87--92 \\
                 6. Useful Orthogonal Matrices (Tools of the Trade) /
                 93--118 \\
                 7. Tridiagonal Form / 119--150 \\
                 8. The $Q L$ and $Q R$ Algorithms / 151--188 \\
                 9. Jacobi Methods / 189--200 \\
                 10. Eigenvalue Bounds / 201--227 \\
                 11. Approximations from a Subspace / 229--260 \\
                 12. Krylov Subspaces / 261--286 \\
                 13. Lanczos Algorithms / 287--321 \\
                 14. Subspace Iteration / 323--337 \\
                 15. The General Linear Eigenvalue Problem / 339--368
                 \\
                 Appendix A: Rank-One and Elementary Matrices / 369--370
                 \\
                 Appendix B: Chebyshev Polynomials / 371--373 \\
                 Back Matter / 375--398 (23 pages)",
}

@Book{Parshall:2006:JJS,
  author =       "Karen Hunger Parshall",
  title =        "{James Joseph Sylvester}: {Jewish} Mathematician in a
                 {Victorian} World",
  publisher =    pub-JOHNS-HOPKINS,
  address =      pub-JOHNS-HOPKINS:adr,
  pages =        "xiii + 461",
  year =         "2006",
  ISBN =         "0-8018-8291-5",
  ISBN-13 =      "978-0-8018-8291-3",
  LCCN =         "QA29.S96 P375 2006",
  MRclass =      "01A70 (01A60)",
  MRnumber =     "2216541 (2007a:01013)",
  MRreviewer =   "Craig G. Fraser",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/bjhs2000.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0625/2005052035-b.html;
                 http://www.loc.gov/catdir/enhancements/fy0625/2005052035-d.html;
                 http://www.loc.gov/catdir/toc/fy0701/2005052035.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1955--",
  subject =      "Sylvester, James Joseph; Mathematicians; Great
                 Britain; History; 19th century; Biography; Jews",
  subject-dates = "1814--1897",
  tableofcontents = "Acknowledgments / xi \\
                 Introduction \\
                 James Joseph Sylvester: The Myth, the Mathematician,
                 the Man / 1 \\
                 Chapter 1 \\
                 Born to ``the Faith in Which the Founder of
                 Christianity Was Educated'' / 9 \\
                 The Josephs of Liverpool / 11 \\
                 The Abraham Joseph Family of London / 16 \\
                 The Royal Institution School, Liverpool / 22 \\
                 Chapter 2 \\
                 A Price of Dissent / 26 \\
                 Cambridge Debates Dissent / 27 \\
                 Within the Walls of St. Johns / 29 \\
                 A Two-Year Hiatus / 36 \\
                 Back at St. John's / 38 \\
                 The 1837 Tripos / 43 \\
                 Chapter 3 \\
                 The Hollow Walls of Academe / 49 \\
                 An Unexpected Opportunity / 51 \\
                 Professor of Natural Philosophy at University College
                 London / 55 \\
                 Looking beyond England / 64 \\
                 Professor of Mathematics at the University of Virginia
                 / 69 \\
                 Struggling against an ``Adverse Tide of Affairs'' / 76
                 \\
                 Chapter 4 \\
                 Actuary by Day \ldots{} Mathematician by Night / 8 \\
                 The Actuary: An Emergent ``Professional Man'' / 83 \\
                 7. J. J. Sylvester, Esq., M.A., F.R.S., Actuary and
                 Secretary / 85 \\
                 The Institute of Actuaries / 92 \\
                 Divided Loyalties: Mathematician or Actuary? / 94 \\
                 Establishing a Mathematical Routine / 101 \\
                 Chapter 5 \\
                 Into the Invariant-Theoretic Unknown / 107 \\
                 The Emergence of a Theory of Invariants / 107 \\
                 Crafting the ``New Algebra'' / 112 \\
                 The Problem of Syzygies / 122 \\
                 From Actuary to Academic? / 130 \\
                 Chapter 6 \\
                 A New Beginning / 137 \\
                 Changing Responsibilities / 138 \\
                 The Royal Military Academy, Woolwich / 144 \\
                 Professor of Mathematics Once More / 147 \\
                 A Roving Mathematical Eye / 156 \\
                 Chapter 7 \\
                 At War with the Military / 161 \\
                 First Battle / 161 \\
                 Temporary Truce / 165 \\
                 Second Battle / 171 \\
                 Hard Won Victories / 176 \\
                 Chapter 8 \\
                 The Uneasy Years / 192 \\
                 Victorian England and Educational Reform / 192 \\
                 Reform and the Royal Military Academy, Woolwich / 196
                 \\
                 Mathematics Misrepresented and Misunderstood: Taking on
                 Huxley / 201 \\
                 The BAAS and Science Education / 206 \\
                 Poetry Soothes the Soul / 211 \\
                 Life after Woolwich / 215 \\
                 New Possibilities on the Horizon? / 219 \\
                 Chapter 9 \\
                 Exploring Familiar Ground on Unfamiliar Territory / 225
                 \\
                 First Impressions / 226 \\
                 Getting Started / 229 \\
                 Thriving in the Graduate Classroom / 235 \\
                 Launching the \booktitle{American Journal of
                 Mathematics} / 239 \\
                 Sustaining the \booktitle{American Journal of
                 Mathematics} / 243 \\
                 Chapter 10 \\
                 Tackling New Challenges in a Home Away from Home / 249
                 \\
                 Sylvester and His Early Students / 249 \\
                 From Invariant Theory to the Theory of Numbers / 254
                 \\
                 From Number Theory to ``Universal Algebra'' / 262 \\
                 A Troubled Transition to the Theory of Partitions / 267
                 \\
                 Henry Smith Is Dead / 273 \\
                 Chapter 11 \\
                 A Bittersweet Victory / 278 \\
                 An Oxford in Transition / 279 \\
                 Between To Worlds / 285 \\
                 A Rocky Year / 293 \\
                 Hopkins in Oxfordshire? / 296 \\
                 Chapter 12 \\
                 The Final Transition / 304 \\
                 Increasing Signs of Age / 305 \\
                 An International Competition / 313 \\
                 A Stead Decline / 317 \\
                 The Final Years / 326 \\
                 Epilogue \\
                 James Joseph Sylvester: The Man and His Legacies / 329
                 \\
                 Notes / 339 \\
                 References / 419 \\
                 Index / 447",
}

@Book{Perlis:1952:TM,
  author =       "Sam Perlis",
  title =        "Theory of Matrices",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xiv + 237",
  year =         "1952",
  LCCN =         "QA263 .P4",
  MRclass =      "09.0X",
  MRnumber =     "0048384 (14,6a)",
  MRreviewer =   "D. E. Rutherford",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Perlis:1991:TM,
  author =       "Sam Perlis",
  title =        "Theory of Matrices",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xiv + 237",
  year =         "1991",
  ISBN =         "0-486-66810-X (paperback)",
  ISBN-13 =      "978-0-486-66810-9 (paperback)",
  LCCN =         "QA188 .P42 1991",
  bibdate =      "Sun Nov 23 10:35:43 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover031/91019037.html",
  acknowledgement = ack-nhfb,
  author-dates = "1913--",
  remark =       "Reprint of \cite{Perlis:1952:TM}.",
  subject =      "Matrices",
}

@Book{Pringle:1971:GIMa,
  author =       "R. M. Pringle and Arthur Asquith Rayner",
  title =        "Generalized Inverse Matrices with Applications to
                 Statistics",
  volume =       "28",
  publisher =    "Griffin",
  address =      "London, UK",
  pages =        "viii + 127",
  year =         "1971",
  ISBN =         "0-85264-181-8",
  ISBN-13 =      "978-0-85264-181-1",
  LCCN =         "QA279 .P74 1971b",
  bibdate =      "Fri Nov 21 08:47:08 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Griffin's statistical monographs and courses",
  acknowledgement = ack-nhfb,
  remark =       "Based on R. M. Pringle's thesis, University of Natal,
                 South Africa",
  subject =      "Analysis of variance; Matrix inversion",
}

@Book{Pringle:1971:GIMb,
  author =       "R. M. Pringle and Arthur Asquith Rayner",
  title =        "Generalized Inverse Matrices with Applications to
                 Statistics",
  volume =       "28",
  publisher =    "Hafner Pub. Co.",
  address =      "New York, NY, USA",
  pages =        "viii + 127",
  year =         "1971",
  LCCN =         "QA279 .P74",
  bibdate =      "Fri Nov 21 08:47:08 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Griffin's statistical monographs and courses",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht000763299.pdf",
  acknowledgement = ack-nhfb,
  subject =      "Analysis of variance; Matrix inversion",
  tableofcontents = "1 Definitions and Some Preliminary Results / 1 \\
                 1.1 Notation and general introduction / 1 \\
                 1.2 The generalized inverse / 3 \\
                 1.3 One-condition generalized inverses / 6 \\
                 1.4 Solution of linear equations / 9 \\
                 1.5 Two-condition generalized inverses / 12 \\
                 1.6 Three-condition generalized inverses / 15 \\
                 1.7 Discussion / 15 \\
                 2 Theoretical Properties of Generalized Inverses / 17
                 \\
                 2.1 Introduction / 17 \\
                 2.2 Results on rank and idempotency / 17 \\
                 2.3 Results on symmetry / 18 \\
                 2.4 Commuting generalized inverses / 19 \\
                 2.5 Latent roots and vectors / 23 \\
                 2.6 Relationships between types of generalized inverses
                 / 24 \\
                 2.7 Generalized inverses of product matrices / 30 \\
                 2.8 Special results on $g_1$-inverses / 32 \\
                 2.9 Miscellaneous results / 35 \\
                 3 Generalized Inverses of Partitioned and Bordered
                 Matrices / 37 \\
                 3.1 Introduction / 37 \\
                 3.2 Matrices partitioned into two submatrices / 38 \\
                 3.3 Partitioned positive semidefinite matrices / 45 \\
                 3.4 Bordered matrices / 48 \\
                 3.5 Some remarks on generalized inverses of partitioned
                 and bordered matrices / 53 \\
                 4 Methods of Computing Generalized Inverses / 55 \\
                 4.1 Introduction / 55 \\
                 4.2 The $g$-inverse / 56 \\
                 4.3 $g_1$-inverses / 61 \\
                 4.4 $g_2$-inverses / 66 \\
                 4.5 $g_3$-inverses / 67 \\
                 4.6 The Cholesky technique / 67 \\
                 5 Singular Normal Variates / 70 \\
                 5.1 Conditional means and variances of the normal
                 multivariate distribution / 70 \\
                 5.2 Regression properties of the multivariate normal
                 distribution / 72 \\
                 5.3 Reversible transformations of singular to
                 nonsingular variates / 74 \\
                 5.4 Conditions for a second-degree polynomial in normal
                 variates to have noncentral $\chi^2$ distribution / 77
                 \\
                 6 The Linear Model of Less Than Full Rank / 80 \\
                 6.1 Introduction / 80 \\
                 6.2 Estimable linear functions / 81 \\
                 6.3 The method of imposed linear restrictions / 90 \\
                 6.4 Relationship between estimability and linear
                 restrictions / 93 \\
                 6.5 Linear models with a priori linear constraints / 98
                 \\
                 6.6 Some aspects of partitioned linear models / 101 \\
                 6.7 Some statistical interpretations of $g$-inverses in
                 linear estimation procedures / 106 \\
                 7 The Linear Model with Singular Variance Matrix / 109
                 \\
                 7.1 Introduction / 109 \\
                 7.2 The Goldman--Zelen method / 110 \\
                 7.3 The Zyskind--Martin method / 114 \\
                 Concluding Remarks / 118 \\
                 References / 119 \\
                 Index / 125",
}

@Book{Radjavi:2000:ST,
  author =       "Heydar Radjavi and Peter Rosenthal",
  title =        "Simultaneous Triangularization",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 318",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4612-1200-3",
  ISBN =         "0-387-98467-4 (hardcover), 0-387-98466-6 (paperback),
                 1-4612-1200-6 (e-book)",
  ISBN-13 =      "978-0-387-98467-4 (hardcover), 978-0-387-98466-7
                 (paperback), 978-1-4612-1200-3 (e-book)",
  LCCN =         "QA197 .R33 2000",
  MRclass =      "47-02 (15-02 15A21 47A15 47D03)",
  MRnumber =     "1736065 (2001e:47001)",
  MRreviewer =   "Donald W. Hadwin",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Universitext",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0815/99023772-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0815/99023772-t.html",
  abstract =     "A collection of matrices is said to be
                 triangularizable if there is an invertible matrix $S$
                 such that $ S^{-1} A S$ is upper triangular for every
                 $A$ in the collection. This generalization of
                 commutativity is the subject of many classical theorems
                 due to Engel, Kolchin, Kaplansky, McCoy and others. The
                 concept has been extended to collections of bounded
                 linear operators on Banach spaces: such a collection is
                 defined to be triangularizable if there is a maximal
                 chain of subspaces of the Banach space, each of which
                 is invariant under every member of the collection. Most
                 of the classical results have been generalized to
                 compact operators, and there are also recent theorems
                 in the finite-dimensional case. This book is the first
                 comprehensive treatment of triangularizability in both
                 the finite and infinite-dimensional cases. It contains
                 numerous very recent results and new proofs of many of
                 the classical theorems. It provides a thorough
                 background for research in both the linear-algebraic
                 and operator-theoretic aspects of triangularizability
                 and related areas. More generally, the book will be
                 useful to anyone interested in matrices or operators,
                 as many of the results are linked to other topics such
                 as spectral mapping theorems, properties of spectral
                 radii and traces, and the structure of semigroups and
                 algebras of operators. It is essentially self-contained
                 modulo solid courses in linear algebra (for the first
                 half) and functional analysis (for the second half),
                 and is therefore suitable as a text or reference for a
                 graduate course.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  shorttableofcontents = "1: Algebras of Matrices \\
                 2: Semigroups of Matrices \\
                 3: Semigroups over fields of Characteristic Zero \\
                 4: Semigroups of Non-negative Matrices \\
                 5: Compact Operators and Invariant Subspaces \\
                 6: Algebras of Compact Operators \\
                 7: Semigroups of Compact Operators \\
                 8: Bounded Operators",
  tableofcontents = "Preface / vii \\
                 Chapter One: Algebras of Matrices / 1 \\
                 1.1 The Triangularization Lemma / 1 \\
                 1.2 Burnside's Theorem / 4 \\
                 1.3 Triangularizability of Algebras of Matrices / 6 \\
                 1.4 Triangularization and the Radical / 10 \\
                 1.5 Block Triangularization and Characterizations of
                 Triangularizability / 12 \\
                 1.6 Approximate Commutativity / 17 \\
                 1.7 Nonassociative Algebras / 21 \\
                 1.8 Notes and Remarks / 25 \\
                 Chapter Two: Semigroups of Matrices / 27 \\
                 2.1 Basic Definitions and Propositions / 27 \\
                 2.2 Permutable Trace / 33 \\
                 2.3 Zero--One Spectra / 36 \\
                 2.4 Notes and Remarks / 41 \\
                 Chapter Three: Spectral Conditions on Semigroups / 43
                 \\
                 3.1 Reduction to the Field of Complex Numbers / 43 \\
                 3.2 Permutable Spectrum / 51 \\
                 3.3 Submultiplicative Spectrum / 55 \\
                 3.4 Conditions on Spectral Radius / 62 \\
                 3.5 The Dominance Condition on Spectra / 70 \\
                 3.6 Notes and Remarks / 73 \\
                 Chapter Four: Finiteness Lemmas and Further Spectral
                 Conditions / 75 \\
                 4.1 Reductions to Finite Semigroups / 75 \\
                 4.2 Subadditive and Sublinear Spectra / 80 \\
                 4.3 Further Multiplicative Conditions on Spectra / 89
                 \\
                 4.4 Polynomial Conditions on Spectra / 93 \\
                 4.5 Notes and Remarks / 102 \\
                 Chapter Five: Semigroups of Nonnegative Matrices / 104
                 \\
                 5.1 Decomposability / 104 \\
                 5.2 Indecomposable Semigroups / 115 \\
                 5.3 Connections with Reducibility / 127 \\
                 5.4 Notes and Remarks / 129 \\
                 Chapter Six: Compact Operators and Invariant Subspaces
                 / 130 \\
                 6.1 Operators on Banach Spaces / 130 \\
                 6.2 Compact Operators / 133 \\
                 6.3 Invariant Subspaces for Compact Operators / 135 \\
                 6.4 The Riesz Decomposition of Compact Operators / 138
                 \\
                 6.5 Trace-Class Operators on Hilbert Space / 142 \\
                 6.6 Notes and Remarks / 149 \\
                 Chapter Seven: Algebras of Compact Operators / 151 \\
                 7.1 The Definition of Triangularizability / 151 \\
                 7.2 Spectra from Triangular Forms / 155 \\
                 7.3 Lomonosov's Lemma and McCoy's Theorem / 162 \\
                 7.4 Transitive Algebras / 167 \\
                 7.5 Block Triangularization and Applications / 173 \\
                 7.6 Approximate Commutativity / 183 \\
                 7.7 Notes and Remarks / 189 \\
                 Chapter Eight: Semigroups of Compact Operators / 193
                 \\
                 8.1 Quasinilpotent Compact Operators / 193 \\
                 8.2 A General Approach / 199 \\
                 8.3 Permutability and Submultiplicativity of Spectra /
                 205 \\
                 8.4 Subadditivity and Sublinearity of Spectra / 209 \\
                 8.5 Polynomial Conditions on Spectra / 213 \\
                 8.6 Conditions on Spectral Radius and Trace / 216 \\
                 8.7 Nonnegative Operators / 223 \\
                 8.8 Notes and Remarks / 241 \\
                 Chapter Nine: Bounded Operators / 244 \\
                 9.1 Collections of Nilpotent Operators / 244 \\
                 9.2 Commutators of Rank One / 250 \\
                 9.3 Bands / 262 \\
                 9.4 Nonnegative Operators / 272 \\
                 9.5 Notes and Remarks / 281 \\
                 References / 284 \\
                 Notation Index / 307 \\
                 Author Index / 309 \\
                 Subject Index / 315",
}

@Book{Rogers:1980:MD,
  author =       "Gerald Stanley Rogers",
  title =        "Matrix Derivatives",
  volume =       "2",
  publisher =    pub-DEKKER,
  address =      pub-DEKKER:adr,
  pages =        "v + 209",
  year =         "1980",
  ISBN =         "0-8247-1176-9 (paperback)",
  ISBN-13 =      "978-0-8247-1176-4 (paperback)",
  LCCN =         "QA188 .R63",
  MRclass =      "62H99 (15A99)",
  MRnumber =     "598276 (83b:62121)",
  MRreviewer =   "D. S. Tracy",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Lecture Notes in Statistics",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht002508073.pdf",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface / iii \\
                 1: Introduction and Summary / 1 \\
                 2: Some Old Matrix Algebra / 7 \\
                 3: Generalized Inverses / 17 \\
                 4: Some Newer Matrix Algebra / 21 \\
                 5: Notation for Derivatives / 31 \\
                 6: Some Theorems For $\partial y / \partial x$ / 41 \\
                 7: Examples of Basic Derivatives / 49 \\
                 8: Using $J$ and $K$ Matrices / 55 \\
                 9: Exploiting the Attitude of Position / 63 \\
                 10: Derivatives When $X$ Is Symmetric / 79 \\
                 11: Optimization of Scalar Functions / 87 \\
                 12: Examples of Optimization / 93 \\
                 13: Jacobians / 109 \\
                 14: Differentials / 117 \\
                 15: The Operation $(\partial / \partial x')Y$ / 137 \\
                 16: Differentiable Generalized Inverses / 149 \\
                 17: Matrices With Linear Structure / 159 \\
                 18: Matrix Derivatives of Elementary Symmetric
                 Functions / 169 \\
                 Appendix: Infinite Dimensional Matrices / 179 \\
                 References / 191 \\
                 Symbol Index / 199 \\
                 Author Index / 203 \\
                 Subject Index / 207",
}

@Book{Roman:1992:ALA,
  author =       "Steven Roman",
  title =        "Advanced Linear Algebra",
  volume =       "135",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 370",
  year =         "1992",
  DOI =          "https://doi.org/10.1007/978-1-4757-2178-2",
  ISBN =         "1-4757-2180-3, 1-4757-2178-1 (e-book)",
  ISBN-13 =      "978-1-4757-2180-5, 978-1-4757-2178-2 (e-book)",
  ISSN =         "0072-5285",
  ISSN-L =       "0072-5285",
  LCCN =         "QA184-205",
  MRclass =      "15-01, 15A03, 15A04, 15A18, 15A21, 15A63, 16010,
                 54E35, 46C05, 51N10, 05A40",
  bibdate =      "Fri Nov 21 11:53:34 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Graduate Texts in Mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Matrix theory",
  tableofcontents = "Preface // vii \\
                 0: Preliminaries / 1 \\
                 Part 1: Preliminaries. Matrices. Determinants.
                 Polynomials. Functions. Equivalence Relations. Zorn's
                 Lemma. Cardinality. \\
                 Part 2: Algebraic Structures. Groups. Rings. Integral
                 Domains. Ideals and Principal Ideal Domains. Prime
                 Elements. Fields. The Characteristic of a Ring. \\
                 Part 1 Basic Linear Algebra \\
                 1: Vector Spaces / 27 \\
                 Vector Spaces. Subspaces. The Lattice of Subspaces.
                 Direct Sums. Spanning Sets and Linear Independence. The
                 Dimension of a Vector Space. The Row and Column Space
                 of a Matrix. Coordinate Matrices. Exercises. \\
                 2: Linear Transformations / 45 \\
                 Linear Transformations. The Kernel and Image of a
                 Linear Transformation. Isomorphisms. The Rank Plus
                 Nullity Theorem. Linear Transformations from Fn to Fm.
                 Change of Basis Matrices. The Matrix of a Linear
                 Transformation. Change of Bases for Linear
                 Transformations. Equivalence of Matrices. Similarity of
                 Matrices. Invariant Subspaces and Reducing Pairs.
                 Exercises. \\
                 3: The Isomorphism Theorems / 63 \\
                 Quotient Spaces. The First Isomorphism Theorem. The
                 Dimension of a Quotient Space. Additional Isomorphism
                 Theorems. Linear Functionals. Dual Bases. Reflexivity.
                 Annihilators. Operator Adjoints. Exercises. \\
                 4: Modules I / 83 \\
                 Motivation. Modules. Submodules. Direct Sums. Spanning
                 Sets. Linear Independence. Homomorphisms. Free Modules.
                 Summary. Exercises. \\
                 5: Modules II / 97 \\
                 Quotient Modules. Quotient Rings and Maximal Ideals.
                 Noetherian Modules. The Hilbert Basis Theorem.
                 Exercises. \\
                 6: Modules over Principal Ideal Domains / 107 \\
                 Free Modules over a Principal Ideal Domain. Torsion
                 Modules. The Primary Decomposition Theorem. The Cyclic
                 Decomposition Theorem for Primary Modules. Uniqueness.
                 The Cyclic Decomposition Theorem. Exercises. \\
                 7: The Structure of a Linear Operator / 121 \\
                 A Brief Review. The Module Associated with a Linear
                 Operator. Submodules and Invariant Subspaces. Orders
                 and the Minimal Polynomial. Cyclic Submodules and
                 Cyclic Subspaces. Summary. The Decomposition of V. The
                 Rational Canonical Form. Exercises. \\
                 8: Eigenvalues and Eigenvectors / 135 \\
                 The Characteristic Polynomial of an Operator.
                 Eigenvalues and Eigenvectors. The Cayley--Hamilton
                 Theorem. The Jordan Canonical Form. Geometric and
                 Algebraic Multiplicities. Diagonalizable Operators.
                 Projections. The Algebra of Projections. Resolutions of
                 the Identity. Projections and Diagonalizability.
                 Projections and In variance. Exercises. \\
                 9: Real and Complex Inner Product Spaces / 157 \\
                 Introduction. Norm and Distance. Isometrics.
                 Orthogonality. Orthogonal and Orthonormal Sets. The
                 Projection Theorem. The Gram--Schmidt Orthogonalization
                 Process. The Riesz Representation Theorem. Exercises.
                 \\
                 10: The Spectral Theorem for Normal Operators / 175 \\
                 The Adjoint of a Linear Operator. Orthogonal
                 Diagonalizability. Motivation. Self-Adjoint Operators.
                 Unitary Operators. Normal Operators. Orthogonal
                 Diagonalization. Orthogonal Projections. Orthogonal
                 Resolutions of the Identity. The Spectral Theorem.
                 Functional Calculus. Positive Operators. The Polar
                 Decomposition of an Operator. Exercises. \\
                 Part 2 Topics \\
                 11: Metric Vector Spaces / 205 \\
                 Symmetric, Skew-symmetric and Alternate Forms. The
                 Matrix of a Bilinear Form. Quadratic Forms. Linear
                 Functionals. Orthogonality. Orthogonal Complements.
                 Orthogonal Direct Sums. Quotient Spaces. Symplectic
                 Geometry-Hyperbolic Planes. Orthogonal Geometry.
                 Orthogonal Bases. The Structure of an Orthogonal
                 Geometry. Isometries. Symmetries. Witt's Cancellation
                 Theorem. Witt's Extension Theorem. Maximum Hyperbolic
                 Subspaces. Exercises. \\
                 12: Metric Spaces / 239 \\
                 The Definition. Open and Closed Sets. Convergence in a
                 Metric Space. The Closure of a Set. Dense Subsets.
                 Continuity. Completeness. Isometries. The Completion of
                 a Metric Space. Exercises. \\
                 13: Hilbert Spaces / 263 \\
                 A Brief Review. Hilbert Spaces. Infinite Series. An
                 Approximation Problem. Hilbert Bases. Fourier
                 Expansions. A Characterization of Hilbert Bases.
                 Hilbert Dimension. A Characterization of Hilbert
                 Spaces. The Riesz Representation Theorem. Exercises.
                 \\
                 14: Tensor Products / 291 \\
                 Free Vector Spaces. Another Look at the Direct Sum.
                 Bilinear Maps and Tensor Products. Properties of the
                 Tensor Product. The Tensor Product of Linear
                 Transformations. Change of Base Field. Multilinear Map
                 and Iterated Tensor Products. Alternating Maps and
                 Exterior Products. Exercises. \\
                 15: Affine Geometry / 315 \\
                 Affine Geometry. Affine Combinations. Affine Hulls. The
                 Lattice of Flats. Affine Independence. Affine
                 Transformations. Projective Geometry. Exercises. \\
                 16: The Umbral Calculus / 329 \\
                 Formal Power Series. The Umbra! Algebra. Formal Power
                 Series as Linear Operators. Sheffer Sequences. Examples
                 of Sheffer Sequences. Umbra! Operators and Umbral
                 Shifts. Continuous Operators on the Umbral Algebra.
                 Operator Adjoints. Automorphisms of the Umbral Algebra.
                 Derivations of the Umbral Algebra. Exercises. \\
                 References / 353 \\
                 Index of Notation / 355 \\
                 Index / 357",
}

@Book{Roman:2005:ALA,
  author =       "Steven Roman",
  title =        "Advanced Linear Algebra",
  volume =       "135",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xvi + 482",
  year =         "2005",
  DOI =          "https://doi.org/10.1007/0-387-27474-X",
  ISBN =         "0-387-27474-X, 0-387-24766-1",
  ISBN-13 =      "978-0-387-27474-4, 978-0-387-24766-3",
  ISSN =         "0072-5285",
  ISSN-L =       "0072-5285",
  LCCN =         "QA184.2 .R66 2005",
  bibdate =      "Fri Nov 21 11:51:16 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Graduate texts in mathematics",
  abstract =     "This is a graduate textbook covering an especially
                 broad range of topics. The first part of the book
                 contains a careful but rapid discussion of the basics
                 of linear algebra, including vector spaces, linear
                 transformations, quotient spaces, and isomorphism
                 theorems. The author then proceeds to modules,
                 emphasizing a comparison with vector spaces. A thorough
                 discussion of inner product spaces, eigenvalues,
                 eigenvectors, and finite dimensional spectral theory
                 follows, culminating in the finite dimensional spectral
                 theorem for normal operators. The second part of the
                 book is a collection of topics, including metric vector
                 spaces, metric spaces, Hilbert spaces, tensor products,
                 and affine geometry. The last chapter discusses the
                 umbral calculus, an area of modern algebra with
                 important applications.\par

                 The second edition contains two new chapters: a chapter
                 on convexity, separation and positive solutions to
                 linear systems and a chapter on the $ Q R $
                 decomposition, singular values and pseudoinverses.
                 Treatments of tensor products and the umbral calculus
                 have been greatly expanded and discussions of
                 determinants, complexification of a real vector space,
                 Schur's lemma and Gersgorin disks have been
                 added.\par

                 The author is Emeritus Professor of Mathematics, having
                 taught at a number of universities, including MIT, UC
                 Santa Barabara, the University of South Florida, the
                 California State University at Fullerton and UC Irvine.
                 He has written 27 books in mathematics at various
                 levels and 9 books on computing. His interests lie
                 mostly in the areas of algebra, set theory and logic,
                 probability and finance.",
  acknowledgement = ack-nhfb,
  subject =      "Matem{\`a}tica; {\`A}lgebra lineal.",
  tableofcontents = "Vector Spaces \\
                 Linear Transformations \\
                 The Isomorphism Theorems \\
                 Modules I: Basic Properties \\
                 Modules II: Free and Noetherian Modules \\
                 Modules over a Principal Ideal Domain \\
                 The Structure of a Linear Operator \\
                 Eigenvalues and Eigenvectors \\
                 Real and Complex Inner Product Spaces \\
                 Structure Theory for Normal Operators \\
                 Metric Vector Spaces: The Theory of Bilinear Forms \\
                 Metric Spaces \\
                 Hilbert Spaces \\
                 Tensor Products \\
                 Positive Solutions to Linear Systems: Convexity and
                 Separation \\
                 Affine Geometry \\
                 Operator Factorizations: $Q R$ and Singular Value \\
                 The Umbral Calculus \\
                 References \\
                 Index",
}

@Book{Roman:2008:ALA,
  author =       "Steven Roman",
  title =        "Advanced Linear Algebra",
  volume =       "135",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "xviii + 522",
  year =         "2008",
  DOI =          "https://doi.org/10.1007/978-0-387-72831-5",
  ISBN =         "0-387-72828-7, 0-387-72831-7",
  ISBN-13 =      "978-0-387-72828-5, 978-0-387-72831-5",
  ISSN =         "0072-5285",
  ISSN-L =       "0072-5285",
  LCCN =         "QA184 .R66 2008; QA184.2 .R66 2007",
  bibdate =      "Fri Nov 21 11:48:32 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Graduate texts in mathematics",
  URL =          "http://www.gbv.de/dms/bowker/toc/9780387728285.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=1132.15002",
  ZMnumber =     "1132.15002",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  subject =      "Algebras, Linear",
  tableofcontents = "Basic Linear Algebra / 33 \\
                 Vector Spaces / 35 \\
                 Linear Transformations / 59 \\
                 The Isomorphism Theorems / 87 \\
                 Modules I: Basic Properties / 109 \\
                 Modules II: Free and Noetherian Modules / 127 \\
                 Modules over a Principal Ideal Domain / 139 \\
                 The Structure of a Linear Operator / 163 \\
                 Eigenvalues and Eigenvectors / 185 \\
                 Real and Complex Inner Product Spaces / 205 \\
                 Structure Theory for Normal Operators / 227 \\
                 Topics / 257 \\
                 Metric Vector Spaces: The Theory of Bilinear Forms /
                 259 \\
                 Metric Spaces / 301 \\
                 Hilbert Spaces / 325 \\
                 Tensor Products / 355 \\
                 Positive Solutions to Linear Systems: Convexity and
                 Separation / 411 \\
                 Affine Geometry / 427 \\
                 Singular Values and the Moore--Penrose Inverse / 443
                 \\
                 An Introduction to Algebras / 451 \\
                 The Umbral Calculus / 471",
}

@Book{Rudin:1953:PMA,
  author =       "Walter Rudin",
  title =        "Principles of Mathematical Analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "227",
  year =         "1953",
  LCCN =         "QA300 .R8",
  bibdate =      "Sun Nov 23 10:37:21 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "1921--2010",
  subject =      "Calculus; Functions",
}

@Book{Rudin:1964:PMA,
  author =       "Walter Rudin",
  title =        "Principles of Mathematical Analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "ix + 270",
  year =         "1964",
  LCCN =         "QA300 .R8 1964",
  bibdate =      "Sun Nov 23 10:37:21 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "1921--2010",
  subject =      "Mathematical analysis",
}

@Book{Rudin:1976:PMA,
  author =       "Walter Rudin",
  title =        "Principles of Mathematical Analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Third",
  pages =        "x + 342",
  year =         "1976",
  ISBN =         "0-07-054235-X",
  ISBN-13 =      "978-0-07-054235-8",
  LCCN =         "QA300 .R8 1976",
  MRclass =      "26-02",
  MRnumber =     "0385023 (52 \#5893)",
  bibdate =      "Sun Nov 23 10:37:21 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International Series in Pure and Applied Mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0602/75017903-d.html;
                 http://www.loc.gov/catdir/toc/mh031/75017903.html",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1921--2010",
  subject =      "Mathematical analysis",
  tableofcontents = "1: The Real and Complex Number Systems \\
                 Introduction \\
                 Ordered Sets \\
                 Fields \\
                 The Real Field \\
                 The Extended Real Number System \\
                 The Complex Field \\
                 Euclidean Spaces \\
                 Appendix \\
                 Exercises \\
                 2: Basic Topology \\
                 Finite, Countable, and Uncountable Sets \\
                 Metric Spaces \\
                 Compact Sets \\
                 Perfect Sets \\
                 Connected Sets \\
                 Exercises \\
                 3: Numerical Sequences and Series \\
                 Convergent Sequences \\
                 Subsequences \\
                 Cauchy Sequences \\
                 Upper and Lower Limits \\
                 Some Special Sequences \\
                 Series \\
                 Series of Nonnegative Terms \\
                 The Number $e$ \\
                 The Root and Ratio Tests \\
                 Power Series \\
                 Summation by Parts \\
                 Absolute Convergence \\
                 Addition and Multiplication of Series \\
                 Rearrangements \\
                 Exercises \\
                 4: Continuity \\
                 Limits of Functions \\
                 Continuous Functions \\
                 Continuity and Compactness \\
                 Continuity and Connectedness \\
                 Discontinuities \\
                 Monotonic Functions \\
                 Infinite Limits and Limits at Infinity \\
                 Exercises \\
                 5: Differentiation \\
                 The Derivative of a Real Function \\
                 Mean Value Theorems \\
                 The Continuity of Derivatives \\
                 L'Hospital's Rule \\
                 Derivatives of Higher-Order \\
                 Taylor's Theorem \\
                 Differentiation of Vector-valued Functions \\
                 Exercises \\
                 6: The Riemann--Stieltjes Integral \\
                 Definition and Existence of the Integral \\
                 Properties of the Integral \\
                 Integration and Differentiation \\
                 Integration of Vector-valued Functions \\
                 Rectifiable Curves \\
                 Exercises \\
                 7: Sequences and Series of Functions \\
                 Discussion of Main Problem \\
                 Uniform Convergence \\
                 Uniform Convergence and Continuity \\
                 Uniform Convergence and Integration \\
                 Uniform Convergence and Differentiation \\
                 Equicontinuous Families of Functions \\
                 The Stone--Weierstrass Theorem \\
                 Exercises \\
                 8: Some Special Functions \\
                 Power Series \\
                 The Exponential and Logarithmic Functions \\
                 The Trigonometric Functions \\
                 The Algebraic Completeness of the Complex Field \\
                 Fourier Series \\
                 The Gamma Function \\
                 Exercises \\
                 9: Functions of Several Variables \\
                 Linear Transformations \\
                 Differentiation \\
                 The Contraction Principle \\
                 The Inverse Function Theorem \\
                 The Implicit Function Theorem \\
                 The Rank Theorem \\
                 Determinants \\
                 Derivatives of Higher Order \\
                 Differentiation of Integrals \\
                 Exercises \\
                 10: Integration of Differential Forms \\
                 Integration \\
                 Primitive Mappings \\
                 Partitions of Unity \\
                 Change of Variables \\
                 Differential Forms \\
                 Simplexes and Chains \\
                 Stokes' Theorem \\
                 Closed Forms and Exact Forms \\
                 Vector Analysis \\
                 Exercises \\
                 11: The Lebesgue Theory \\
                 Set Functions \\
                 Construction of the Lebesgue Measure \\
                 Measure Spaces \\
                 Measurable Functions \\
                 Simple Functions \\
                 Integration \\
                 Comparison with the Riemann Integral \\
                 Integration of Complex Functions \\
                 Functions of Class L?? \\
                 Exercises \\
                 Bibliography \\
                 List of Special Symbols \\
                 Index",
}

@Book{Seneta:1973:NNMa,
  author =       "Eugene Seneta",
  title =        "Non-Negative Matrices: an Introduction to Theory and
                 Applications",
  publisher =    pub-HALSTED,
  address =      pub-HALSTED:adr,
  pages =        "x + 214",
  year =         "1973",
  ISBN =         "0-470-77605-6",
  ISBN-13 =      "978-0-470-77605-6",
  LCCN =         "QA188 .S46",
  MRclass =      "15A48 (60J10)",
  MRnumber =     "0389944 (52 \#10773)",
  MRreviewer =   "B. Levinger",
  bibdate =      "Sun Nov 23 10:43:18 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1941--",
  remark =       "Later edition published as \cite{Seneta:1981:NNM}.",
  subject =      "Non-negative matrices",
}

@Book{Seneta:1981:NNM,
  author =       "Eugene (Eugene) Seneta",
  title =        "Non-Negative Matrices and {Markov} Chains",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xv + 279",
  year =         "1981",
  ISBN =         "0-387-90598-7 (New York), 3-540-90598-7 (Berlin)",
  ISBN-13 =      "978-0-387-90598-3 (New York), 978-3-540-90598-1
                 (Berlin)",
  LCCN =         "QA188 .S46 1981",
  bibdate =      "Sun Nov 23 10:48:07 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Springer Series in Statistics.",
  URL =          "http://www.gbv.de/dms/bowker/toc/9783540905981.pdf",
  abstract =     "Finite non-negative matrices; Fundamental concepts and
                 results in the theory of non-negative matrices; Some
                 secondary theory with emphasis on irreducible matrices,
                 and applications; Inhomogeneous products of
                 non-negative matrices; Markov chains and finite
                 stochastic matrices; Countable non-negative matrices;
                 Countable stochastic matrices; Countable non-negative
                 matrices; Truncations of infinite stochastic matrices;
                 Appendices; Appendices; Bibliograpy; Index.",
  acknowledgement = ack-nhfb,
  author-dates = "1941--",
  subject =      "Markov, Procesos de; Matrices; Matrix; (Math.);
                 Stochastischer Prozess; Markov-Kette; Markov-Prozess;
                 Nichtnegative Matrix",
  tableofcontents = "Fundamental concepts and results in the theory of
                 non-negative matrices \\
                 Some secondary theory with emphasis on irreducible
                 matrices and applications \\
                 Inhomogeneous products of non-negative matrices \\
                 Markov chains and finite stochastic matrices \\
                 Countable stochastic matrices \\
                 Countable non-negative matrices \\
                 Truncations of infinite stochastic matrices",
}

@Book{Seneta:2006:NNM,
  author =       "E. (Eugene) Seneta",
  title =        "Non-Negative Matrices and {Markov} Chains",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Revised",
  pages =        "xv + 279 + 8",
  year =         "2006",
  ISBN =         "0-387-29765-0 (paperback)",
  ISBN-13 =      "978-0-387-29765-1 (paperback)",
  LCCN =         "QA188 .S46 2006",
  bibdate =      "Sun Nov 23 10:45:29 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Springer series in statistics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0663/2005935207-d.html;
                 http://www.loc.gov/catdir/toc/fy0804/2005935207.html",
  acknowledgement = ack-nhfb,
  author-dates = "1941--",
  subject =      "Non-negative matrices; Markov processes; Matrices non
                 n{\'e}gatives; Markov, Processus de",
  tableofcontents = "Fundamental concepts and results in the theory of
                 non-negative matrices \\
                 Some secondary theory with emphasis on irreducible
                 matrices, and applications \\
                 Inhomogeneous products of non-negative matrices \\
                 Markov chains and finite stochastic matrices \\
                 Countable stochastic matrices \\
                 Countable non-negative matrices \\
                 Truncations of infinity stochastic matrices",
}

@Book{Seneta:1973:NNMc,
  author =       "E. (Eugene) Seneta",
  title =        "Non-Negative Matrices: an Introduction to Theory and
                 Applications",
  publisher =    "Allen and Unwin",
  address =      "London, UK",
  pages =        "x + 214",
  year =         "1973",
  ISBN =         "0-04-519011-9",
  ISBN-13 =      "978-0-04-519011-9",
  LCCN =         "QA188 .S46 1973b",
  bibdate =      "Sun Nov 23 10:43:17 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1941--",
  subject =      "Non-negative matrices",
}

@Book{Serre:2002:MTA,
  author =       "D{\'e}nis Serre",
  title =        "Matrices: Theory and Applications",
  volume =       "216",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 202",
  year =         "2002",
  DOI =          "https://doi.org/10.1007/b98899",
  ISBN =         "0-387-95460-0, 0-387-22758-X (e-book)",
  ISBN-13 =      "978-0-387-95460-8, 978-0-387-22758-0 (e-book)",
  LCCN =         "QA188 .S4713 2002",
  MRclass =      "15-01 (15A18 15A23 65Fxx)",
  MRnumber =     "1923507 (2003h:15001)",
  MRreviewer =   "R. J. Bumcrot",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Translated from the 2001 French original.",
  series =       "Graduate Texts in Mathematics",
  URL =          "http://link.springer.com/book/10.1007/b98899;
                 http://www.loc.gov/catdir/enhancements/fy0817/2002022926-b.html;
                 http://www.loc.gov/catdir/enhancements/fy0817/2002022926-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0817/2002022926-t.html;
                 http://www.springerlink.com/openurl.asp?genre=book&isbn=978-0-387-95460-8",
  abstract =     "In this book, D{\'e}nis Serre begins by providing a
                 clean and concise introduction to the basic theory of
                 matrices. He then goes on to give many interesting
                 applications of matrices to different aspects of
                 mathematics and also other areas of science and
                 engineering. The book mixes together algebra, analysis,
                 complexity theory and numerical analysis. As such, this
                 book will provide many scientists, not just
                 mathematicians, with a useful and reliable reference.
                 It is intended for advanced undergraduate and graduate
                 students with either applied or theoretical goals. This
                 book is based on a course given by the author at the
                 {\'E}cole Normale Sup{\'e}rieure de Lyon.\par

                 D{\'e}nis Serre is Professor of Mathematics at
                 {\'E}cole Normale Sup{\'e}rieure de Lyon and a former
                 member of the Institut Universaire de France. He is a
                 member of numerous editorial boards and the author of
                 Systems of Conservation Laws (Cambridge University
                 Press 2000). The present book is a translation of the
                 original French edition, \booktitle{Les Matrices:
                 Th{\'e}orie et Pratique}, published by Dunod (2001).",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Cover \\
                 Preface \\
                 Table of Contents \\
                 List of Symbols \\
                 1. Elementary Theory \\
                 2. Square Matrices \\
                 3. Matrices with Real or Complex Entries \\
                 4. Norms \\
                 5. Nonnegative Matrices \\
                 6. Matrices with Entries in a Principal Ideal Domain;
                 Jordan Reduction \\
                 7. Exponential of a Matrix, Polar Decomposition, and
                 Classical Groups \\
                 8. Matrix Factorizations \\
                 9. Iterative Methods for Linear Problems \\
                 10. Approximation of Eigenvalues \\
                 References",
}

@Book{Staib:1969:IML,
  author =       "John H. Staib",
  title =        "An Introduction to Matrices and Linear
                 Transformations",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xii + 336",
  year =         "1969",
  LCCN =         "QA251 .S77",
  bibdate =      "Sat Nov 22 18:28:44 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Addison-Wesley series in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Algebras, Linear",
}

@Book{Stewart:1973:IMC,
  author =       "G. W. (Gilbert W.) Stewart",
  title =        "Introduction to Matrix Computations",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiii + 441",
  year =         "1973",
  ISBN =         "0-12-670350-7",
  ISBN-13 =      "978-0-12-670350-4",
  LCCN =         "QA188 .S71 1973",
  MRclass =      "65FXX",
  MRnumber =     "0458818 (56 \#17018)",
  MRreviewer =   "James H. Wilkinson",
  bibdate =      "Sun Nov 23 10:56:10 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Computer Science and Applied Mathematics, Editor:
                 Werner Rheinboldt",
  URL =          "http://catdir.loc.gov/catdir/description/els031/72082636.html;
                 http://catdir.loc.gov/catdir/toc/els031/72082636.html;
                 http://www.gbv.de/dms/hbz/toc/ht000832348.pdf;
                 http://www.loc.gov/catdir/description/els031/72082636.html;
                 http://www.loc.gov/catdir/toc/els031/72082636.html",
  acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah # "
                 and " # ack-crj,
  GWS-number =   "B1",
  subject =      "Matrices; Data processing",
  tableofcontents = "Preface / ix \\
                 Acknowledgments / xiii \\
                 1. Preliminaries \\
                 \\
                 1. The Space $R^n$ / 2 \\
                 2. Linear Independence, Subspaces, and Bases / 9 \\
                 3. Matrices / 20 \\
                 4. Operations with Matrices / 29 \\
                 5. Linear Transformations and Matrices / 46 \\
                 6. Linear Equations and Inverses / 54 \\
                 7. A Matrix Reduction and Some Consequences / 63 \\
                 \\
                 2. Practicalities \\
                 \\
                 1. Errors, Arithmetic, and Stability / 69 \\
                 2. An Informal Language / 83 \\
                 3. Coding Matrix Operations / 93 \\
                 3. The Direct Solution of Linear Systems \\
                 \\
                 1. Triangular Matrices and Systems / 106 \\
                 2. Gaussian Elimination / 113 \\
                 3. Triangular Decomposition / 131 \\
                 4. The Solution of Linear Systems / 144 \\
                 5. The Effects of Rounding Error / 148 \\
                 \\
                 4. Norms, Limits, and Condition Numbers \\
                 \\
                 1. Norms and Limits / 161 \\
                 2. Matrix Norms / 173 \\
                 3. Inverses of Perturbed Matrices / 184 \\
                 4. The Accuracy of Solutions of Linear Systems / 192
                 \\
                 5. Iterative Refinement of Approximate Solutions of
                 Linear Systems / 200 \\
                 \\
                 5. The Linear Least Squares Problem \\
                 1. Orthogonality / 209 \\
                 2. The Linear Least Squares Problem / 217 \\
                 3. Orthogonal Triangularization / 230 \\
                 4. The Iterative Refinement of Least Squares Solutions
                 / 245 \\
                 \\
                 6. Eigenvalues and Eigenvectors \\
                 \\
                 1. The Space $\mathbb{C}^n$ / 251 \\
                 2. Eigenvalues and Eigenvectors / 262 \\
                 3. Reduction of Matrices by Similarity Transformations
                 / 275 \\
                 4. The Sensitivity of Eigenvalues and Eigenvectors /
                 289 \\
                 5. Hermitian Matrices / 307 \\
                 6. The Singular Value Decomposition / 317 \\
                 \\
                 7. The $Q R$ Algorithm \\
                 \\
                 1. Reduction to Hessenberg and Tridiagonal Forms / 328
                 \\
                 2. The Power and Inverse Power Methods / 340 \\
                 3. The Explicitly Shifted $Q R$ Algorithm / 351 \\
                 4. The Implicitly Shifted $Q R$ Algorithm / 368 \\
                 5. Computing Singular Values and Vectors / 381 \\
                 6. The Generalized Eigenvalue Problem $A - \lambda B$ /
                 387 \\
                 \\
                 Appendix 1. The Greek Alphabet and Latin Notational
                 Correspondents / 395 \\
                 \\
                 Appendix 2. Determinants / 396 \\
                 Appendix 3. Rounding-Error Analysis of Solution of
                 Triangular Systems and of Gaussian Elimination / 405
                 \\
                 \\
                 Appendix 4. Of Things Not Treated / 413 \\
                 Bibliography / 417 \\
                 Index of Notation / 425 \\
                 Index of Algorithms / 427 \\
                 Index / 429",
}

@Book{Stewart:1990:MPT,
  author =       "Gilbert Wright (Gilbert W.) Stewart and {Ji-guang}
                 Sun",
  title =        "Matrix Perturbation Theory",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 365",
  year =         "1990",
  ISBN =         "0-12-670230-6 (hardcover)",
  ISBN-13 =      "978-0-12-670230-9 (hardcover)",
  LCCN =         "QA871 .S775 1990",
  bibdate =      "Thu May 29 07:15:52 MDT 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Computer science and scientific computing",
  URL =          "http://www.loc.gov/catdir/description/els032/90033378.htm;
                 http://www.loc.gov/catdir/description/els032/90033378.html;
                 http://www.loc.gov/catdir/toc/els031/90033378.htm;
                 http://www.loc.gov/catdir/toc/els031/90033378.html",
  acknowledgement = ack-nhfb,
  GWS-number =   "B3",
  subject =      "Perturbation (Mathematics); Matrices",
  tableofcontents = "I. Preliminaries \\
                 1. Notation \\
                 2. The $Q R$ decomposition \\
                 projections \\
                 3. Eigenvalues and eigenvectors \\
                 4. The singular value decomposition \\
                 II. Norms and metrics \\
                 1. Vector norms \\
                 2. Matrix norms \\
                 3. Unitarily invariant norms \\
                 4. Metrics on subspaces of C'n' \\
                 III. Linear systems and least squares problems \\
                 1. The pseudo-inverse and least squares \\
                 2. Inverses and linear systems \\
                 3. The pseudo-inverse \\
                 4. Projections \\
                 5. The Linear least squares problem \\
                 IV. The perturbation of Eigenvalues \\
                 1. General perturbation theorems \\
                 2. Gerschgorin theory: differentiability \\
                 3. Normal and diagonalizable matrices \\
                 4. Hermitian matrices \\
                 5. Some further results \\
                 V. Invariant subspaces \\
                 1. The theory of simple invariant subspaces \\
                 2. Perturbation of invariant subspaces \\
                 3. Hermitian matrices \\
                 4. The singular value decomposition \\
                 VI. Generalized Eigenvalue problems \\
                 1. Background \\
                 2. Regular matrix pairs \\
                 3. Definite matrix pairs \\
                 References \\
                 Notation \\
                 Index",
}

@Book{Strutt:1877:TS,
  author =       "John William {Strutt (Baron Rayleigh)}",
  title =        "The Theory of Sound",
  publisher =    pub-MACMILLAN,
  address =      pub-MACMILLAN:adr,
  pages =        "xi + 326 (vol. 1), x + 302 (vol. 2)",
  year =         "1877--1878",
  LCCN =         "QC223 .R26",
  MRclass =      "76.1X",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1842--1919",
}

@Book{Strutt:1894:TS,
  author =       "John William {Strutt (Baron Rayleigh)}",
  title =        "The Theory of Sound",
  publisher =    pub-MACMILLAN,
  address =      pub-MACMILLAN:adr,
  edition =      "Second",
  pages =        "xiv + 480 (vol. 1), xvi + 504 (vol. 2)",
  year =         "1894--1896",
  LCCN =         "QC223 .R26",
  MRclass =      "76.1X",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1842--1919",
}

@Book{Strutt:1945:TS,
  author =       "John William {Strutt (Baron Rayleigh)}",
  title =        "The Theory of Sound",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second",
  pages =        "xlii + 480 (vol. 1), xii + 504 (vol. 2)",
  year =         "1945",
  LCCN =         "QC223 .R26",
  MRclass =      "76.1X",
  MRnumber =     "0016009 (7,500e)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  remark =       "Reprint of \cite{Strutt:1894:TS}.",
}

@Book{Suprunenko:1968:CM,
  author =       "D. A. (Dmitrij Alekseevic) Suprunenko and R. I.
                 (Regina Iosifovna) Tyshkevich",
  title =        "Commutative Matrices",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "viii + 158",
  year =         "1968",
  LCCN =         "QA263 .S913",
  bibdate =      "Fri Nov 21 12:09:35 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  remark =       "English translation by Scripta Technica, Inc. of
                 \booktitle{Perestanovocnije matrici}, Minsk, USSR.",
}

@Book{Tang:2007:MMEa,
  author =       "Kwong-Tin Tang",
  title =        "Mathematical Methods for Engineers and Scientists: 1.
                 Complex Analysis, Determinants and Matrices",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 319",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-3-540-30274-2",
  ISBN =         "3-540-30273-5 (hardcover), 3-540-30274-3 (e-book)",
  ISBN-13 =      "978-3-540-30273-5 (hardcover), 978-3-540-30274-2
                 (e-book)",
  LCCN =         "QA401 .T36 2007",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://d-nb.info/97689131X/04;
                 http://swbplus.bsz-bw.de/bsz261984101cov.htm;
                 http://swbplus.bsz-bw.de/bsz261984101inh.pdf;
                 http://swbplus.bsz-bw.de/bsz261984101kap.pdf;
                 http://swbplus.bsz-bw.de/bsz261984101vlg.htm;
                 http://www.loc.gov/catdir/enhancements/fy0824/2006932619-b.html;
                 http://www.loc.gov/catdir/enhancements/fy0824/2006932619-d.html;
                 http://www.loc.gov/catdir/toc/fy0804/2006932619.html",
  acknowledgement = ack-nhfb,
  author-dates = "1936--",
  subject =      "Mathematical physics; Textbooks; Engineering
                 mathematics; Mathematical models",
  tableofcontents = "Part I Complex Analysis \\
                 1 Complex Numbers / 3 \\
                 1.1 Our Number System / 3 \\
                 1.1.1 Addition and Multiplication of Integers / 4 \\
                 1.1.2 Inverse Operations / 5 \\
                 1.1.3 Negative Numbers / 6 \\
                 1.1.4 Fractional Numbers / 7 \\
                 1.1.5 Irrational Numbers / 8 \\
                 1.1.6 Imaginary Numbers / 9 \\
                 1.2 Logarithm / 13 \\
                 1.2.1 Napier's Idea of Logarithm / 13 \\
                 1.2.2 Briggs' Common Logarithm / 15 \\
                 1.3 A Peculiar Number Called $e$ / 18 \\
                 1.3.1 The Unique Property of $e$ / 18 \\
                 1.3.2 The Natural Logarithm / 19 \\
                 1.3.3 Approximate Value of $e$ / 21 \\
                 1.4 The Exponential Function as an Infinite Series / 21
                 \\
                 1.4.1 Compound Interest / 21 \\
                 1.4.2 The Limiting Process Representing e / 23 \\
                 1.4.3 The Exponential Function ex / 24 \\
                 1.5 Unification of Algebra and Geometry / 24 \\
                 1.5.1 The Remarkable Euler Formula / 24 \\
                 1.5.2 The Complex Plane / 25 \\
                 1.6 Polar Form of Complex Numbers / 28 \\
                 1.6.1 Powers and Roots of Complex Numbers / 30 \\
                 1.6.2 Trigonometry and Complex Numbers / 33 \\
                 1.6.3 Geometry and Complex Numbers / 40 \\
                 1.7 Elementary Functions of Complex Variable / 46 \\
                 1.7.1 Exponential and Trigonometric Functions of $z$ /
                 46 \\
                 1.7.2 Hyperbolic Functions of $z$ / 48 \\
                 1.7.3 Logarithm and General Power of $z$ / 50 \\
                 1.7.4 Inverse Trigonometric and Hyperbolic Functions /
                 55 \\
                 Exercises / 58 \\
                 2 Complex Functions / 61 \\
                 2.1 Analytic Functions / 61 \\
                 2.1.1 Complex Function as Mapping Operation / 62 \\
                 2.1.2 Differentiation of a Complex Function / 62 \\
                 2.1.3 Cauchy--Riemann Conditions / 65 \\
                 2.1.4 Cauchy--Riemann Equations in Polar Coordinates /
                 67 \\
                 2.1.5 Analytic Function as a Function of $z$ Alone / 69
                 \\
                 2.1.6 Analytic Function and Laplace's Equation / 74 \\
                 2.2 Complex Integration / 81 \\
                 2.2.1 Line Integral of a Complex Function / 81 \\
                 2.2.2 Parametric Form of Complex Line Integral / 84 \\
                 2.3 Cauchy's Integral Theorem / 87 \\
                 2.3.1 Green's Lemma / 87 \\
                 2.3.2 Cauchy--Goursat Theorem / 89 \\
                 2.3.3 Fundamental Theorem of Calculus / 90 \\
                 2.4 Consequences of Cauchy's Theorem / 93 \\
                 2.4.1 Principle of Deformation of Contours / 93 \\
                 2.4.2 The Cauchy Integral Formula / 94 \\
                 2.4.3 Derivatives of Analytic Function / 96 \\
                 Exercises / 103 \\
                 3 Complex Series and Theory of Residues / 107 \\
                 3.1 A Basic Geometric Series / 107 \\
                 3.2 Taylor Series / 108 \\
                 3.2.1 The Complex Taylor Series / 108 \\
                 3.2.2 Convergence of Taylor Series / 109 \\
                 3.2.3 Analytic Continuation / 111 \\
                 3.2.4 Uniqueness of Taylor Series / 112 \\
                 3.3 Laurent Series / 117 \\
                 3.3.1 Uniqueness of Laurent Series / 120 \\
                 3.4 Theory of Residues / 126 \\
                 3.4.1 Zeros and Poles / 126 \\
                 3.4.2 Definition of the Residue / 128 \\
                 3.4.3 Methods of Finding Residues / 129 \\
                 3.4.4 Cauchy's Residue Theorem / 133 \\
                 3.4.5 Second Residue Theorem / 134 \\
                 3.5 Evaluation of Real Integrals with Residues / 141
                 \\
                 3.5.1 Integrals of Trigonometric Functions / 141 \\
                 3.5.2 Improper Integrals I: Closing the Contour with a
                 Semicircle at Infinity / 144 \\
                 3.5.3 Fourier Integral and Jordan's Lemma / 147 \\
                 3.5.4 Improper Integrals II: Closing the Contour with
                 Rectangular and Pie-shaped Contour / 153 \\
                 3.5.5 Integration Along a Branch Cut / 158 \\
                 3.5.6 Principal Value and Indented Path Integrals / 160
                 \\
                 Exercises / 165 \\
                 Part II Determinants and Matrices \\
                 4 Determinants / 173 \\
                 4.1 Systems of Linear Equations / 173 \\
                 4.1.1 Solution of Two Linear Equations / 173 \\
                 4.1.2 Properties of Second-Order Determinants / 175 \\
                 4.1.3 Solution of Three Linear Equations / 175 \\
                 4.2 General Definition of Determinants / 179 \\
                 4.2.1 Notations / 179 \\
                 4.2.2 Definition of a $n$th Order Determinant / 181 \\
                 4.2.3 Minors, Cofactors / 183 \\
                 4.2.4 Laplacian Development of Determinants by a Row
                 (or a Column) / 184 \\
                 4.3 Properties of Determinants / 188 \\
                 4.4 Cramer's Rule / 193 \\
                 4.4.1 Nonhomogeneous Systems / 193 \\
                 4.4.2 Homogeneous Systems / 195 \\
                 4.5 Block Diagonal Determinants / 196 \\
                 4.6 Laplacian Developments by Complementary Minors /
                 198 \\
                 4.7 Multiplication of Determinants of the Same Order /
                 202 \\
                 4.8 Differentiation of Determinants / 203 \\
                 4.9 Determinants in Geometry / 204 \\
                 Exercises / 208 \\
                 5 Matrix Algebra / 213 \\
                 5.1 Matrix Notation / 213 \\
                 5.1.1 Definition / 213 \\
                 5.1.2 Some Special Matrices / 214 \\
                 5.1.3 Matrix Equation / 216 \\
                 5.1.4 Transpose of a Matrix / 218 \\
                 5.2 Matrix Multiplication / 220 \\
                 5.2.1 Product of Two Matrices / 220 \\
                 5.2.2 Motivation of Matrix Multiplication / 223 \\
                 5.2.3 Properties of Product Matrices / 225 \\
                 5.2.4 Determinant of Matrix Product / 230 \\
                 5.2.5 The Commutator / 232 \\
                 5.3 Systems of Linear Equations / 233 \\
                 5.3.1 Gauss Elimination Method / 234 \\
                 5.3.2 Existence and Uniqueness of Solutions of Linear
                 Systems / 237 \\
                 5.4 Inverse Matrix / 241 \\
                 5.4.1 Nonsingular Matrix / 241 \\
                 5.4.2 Inverse Matrix by Cramer's Rule / 243 \\
                 5.4.3 Inverse of Elementary Matrices / 246 \\
                 5.4.4 Inverse Matrix by Gauss--Jordan Elimination / 248
                 \\
                 Exercises / 250 \\
                 6 Eigenvalue Problems of Matrices / 255 \\
                 6.1 Eigenvalues and Eigenvectors / 255 \\
                 6.1.1 Secular Equation / 255 \\
                 6.1.2 Properties of Characteristic Polynomial / 262 \\
                 6.1.3 Properties of Eigenvalues / 265 \\
                 6.2 Some Terminology / 266 \\
                 6.2.1 Hermitian Conjugation / 267 \\
                 6.2.2 Orthogonality / 268 \\
                 6.2.3 Gram--Schmidt Process / 269 \\
                 6.3 Unitary Matrix and Orthogonal Matrix / 271 \\
                 6.3.1 Unitary Matrix / 271 \\
                 6.3.2 Properties of Unitary Matrix. / 272 \\
                 6.3.3 Orthogonal Matrix / 273 \\
                 6.3.4 Independent Elements of an Orthogonal Matrix /
                 274 \\
                 6.3.5 Orthogonal Transformation and Rotation Matrix /
                 275 \\
                 6.4 Diagonalization / 78 \\
                 6.4.1 Similarity Transformation / 278 \\
                 6.4.2 Diagonalizing a Square Matrix / 281 \\
                 6.4.3 Quadratic Forms / 284 \\
                 6.5 Hermitian Matrix and Symmetric Matrix / 286 \\
                 6.5.1 Definitions / 286 \\
                 6.5.2 Eigenvalues of Hermitian Matrix / 287 \\
                 6.5.3 Diagonalizing a Hermitian Matrix / 288 \\
                 6.5.4 Simultaneous Diagonalization / 296 \\
                 6.6 Normal Matrix / 298 \\
                 6.7 Functions of a Matrix / 300 \\
                 6.7.1 Polynomial Functions of a Matrix / 300 \\
                 6.7.2 Evaluating Matrix Functions by Diagonalization /
                 301 \\
                 6.7.3 The Cayley--Hamilton Theorem / 305 \\
                 Exercises / 309 \\
                 References / 313 \\
                 Index / 315",
}

@Book{Tang:2007:MMEb,
  author =       "Kwong-Tin Tang",
  title =        "Mathematical Methods for Engineers and Scientists: 2.
                 Vector Analysis, Ordinary Differential Equations and
                 {Laplace} Transforms",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 339",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-3-540-30270-4",
  ISBN =         "3-540-30268-9 (hardcover), 3-540-30270-0 (e-book)",
  ISBN-13 =      "978-3-540-30268-1 (hardcover), 978-3-540-30270-4
                 (e-book)",
  LCCN =         "QA401 .T36 2007",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://d-nb.info/976891336/04",
  acknowledgement = ack-nhfb,
  author-dates = "1936--",
  subject =      "Mathematical physics; Textbooks; Engineering
                 mathematics; Mathematical models",
  tableofcontents = "Part I Vector Analysis \\
                 Vectors / 3 \\
                 1.1 Bound and Free Vectors / 4 \\
                 1.2 Vector Operations / 4 \\
                 1.2.1 Multiplication by a Scalar / 5 \\
                 1.2.2 Unit Vector / 5 \\
                 1.2.3 Addition and Subtraction / 5 \\
                 1.2.4 Dot Product / 6 \\
                 1.2.5 Vector Components / 10 \\
                 1.2.6 Cross Product / 13 \\
                 1.2.7 Triple Products / 17 \\
                 1.3 Lines and Planes / 23 \\
                 1.3.1 Straight Lines / 23 \\
                 1.3.2 Planes in Space / 27 \\
                 Exercises / 31 \\
                 Vector Calculus / 35 \\
                 2.1 The Time Derivative / 36 \\
                 2.1.1 Velocity and Acceleration / 36 \\
                 2.1.2 Angular Velocity Vector / 37 \\
                 2.2 Differentiation in Noninertial Reference Systems /
                 42 \\
                 2.3 Theory of Space Curve / 47 \\
                 2.4 The Gradient Operator / 51 \\
                 2.4.1 The Gradient of a Scalar Function / 51 \\
                 2.4.2 Geometrical Interpretation of Gradient / 53 \\
                 2.4.3 Line Integral of a Gradient Vector / 56 \\
                 2.5 The Divergence of a Vector / 61 \\
                 2.5.1 The Flux of a Vector Field / 62 \\
                 2.5.2 Divergence Theorem / 65 \\
                 2.5.3 Continuity Equation / 69 \\
                 2.6 The Curl of a Vector / 70 \\
                 2.6.1 Stokes' Theorem / 71 \\
                 2.7 Further Vector Differential Operations / 78 \\
                 2.7.1 Product Rules / 79 \\
                 2.7.2 Second Derivatives / 81 \\
                 2.8 Further Integral Theorems / 85 \\
                 2.8.1 Green's Theorem / 85 \\
                 2.8.2 Other Related Integrals / 86 \\
                 2.9 Classification of Vector Fields / 89 \\
                 2.9.1 Irrotational Field and Scalar Potential / 89 \\
                 2.9.2 Solenoidal Field and Vector Potential / 92 \\
                 2.10 Theory of Vector Fields / 95 \\
                 2.10.1 Functions of Relative Coordinates / 95 \\
                 2.10.2 Divergence of $\mathbb{R} / |R|^2$ as a Delta
                 Function / 98 \\
                 2.10.3 Helmholtz's Theorem / 101 \\
                 2.10.4 Poisson's and Laplace's Equations / 104 \\
                 2.10.5 Uniqueness Theorem / 105 \\
                 Exercises / 106 \\
                 3 Curved Coordinates / 113 \\
                 3.1 Cylindrical Coordinates / 113 \\
                 3.1.1 Differential Operations / 116 \\
                 3.1.2 Infinitesimal Elements / 120 \\
                 3.2 Spherical Coordinates / 122 \\
                 3.2.1 Differential Operations / 125 \\
                 3.2.2 Infinitesimal Elements / 128 \\
                 3.3 General Curvilinear Coordinate System / 130 \\
                 3.3.1 Coordinate Surfaces and Coordinate Curves / 130
                 \\
                 3.3.2 Differential Operations in Curvilinear Coordinate
                 Systems / 133 \\
                 3.4 Elliptical Coordinates / 138 \\
                 3.4.1 Coordinate Surfaces / 139 \\
                 3.4.2 Relations with Rectangular Coordinates / 141 \\
                 3.4.3 Prolate Spheroidal Coordinates / 144 \\
                 3.5 Multiple Integrals / 144 \\
                 3.5.1 Jacobian for Double Integral / 145 \\
                 3.5.2 Jacobians for Multiple Integrals / 147 \\
                 Exercises / 150 \\
                 4 Vector Transformation and Cartesian Tensors / 155 \\
                 4.1 Transformation Properties of Vectors / 156 \\
                 4.1.1 Transformation of Position Vector / 156 \\
                 4.1.2 Vector Equations / 158 \\
                 4.1.3 Euler Angles / 159 \\
                 4.1.4 Properties of Rotation Matrices / 162 \\
                 4.1.5 Definition of a Scalar and a Vector in Terms of
                 Transformation Properties / 165 \\
                 4.2 Cartesian Tensors / 169 \\
                 4.2.1 Definition / 169 \\
                 4.2.2 Kronecker and Levi-Civit{\`a} Tensors / 171 \\
                 4.2.3 Outer Product / 174 \\
                 4.2.4 Contraction / 176 \\
                 4.2.5 Summation Convention / 177 \\
                 4.2.6 Tensor Fields / 179 \\
                 4.2.7 Quotient Rule / 182 \\
                 4.2.8 Symmetry Properties of Tensors / 183 \\
                 4.2.9 Pseudotensors / 185 \\
                 4.3 Some Physical Examples / 189 \\
                 4.3.1 Moment of Inertia Tensor / 189 \\
                 4.3.2 Stress Tensor / 190 \\
                 4.3.3 Strain Tensor and Hooke's Law / 193 \\
                 Exercises / 195 \\
                 Part II Differential Equations and Laplace Transforms
                 \\
                 5 Ordinary Differential Equations / 201 \\
                 5.1 First-Order Differential Equations / 201 \\
                 5.1.1 Equations with Separable Variables / 202 \\
                 5.1.2 Equations Reducible to Separable Type / 204 \\
                 5.1.3 Exact Differential Equations / 205 \\
                 5.1.4 Integrating Factors / 207 \\
                 5.2 First-Order Linear Differential Equations / 210 \\
                 5.2.1 Bernoulli Equation / 213 \\
                 5.3 Linear Differential Equations of Higher Order / 214
                 \\
                 5.4 Homogeneous Linear Differential Equations with
                 Constant Coefficients / 216 \\
                 5.4.1 Characteristic Equation with Distinct Roots / 217
                 \\
                 5.4.2 Characteristic Equation with Equal Roots / 218
                 \\
                 5.4.3 Characteristic Equation with Complex Roots / 218
                 \\
                 5.5 Nonhomogeneous Linear Differential Equations with
                 Constant Coefficients / 222 \\
                 5.5.1 Method of Undetermined Coefficients / 222 \\
                 5.5.2 Use of Complex Exponentials / 229 \\
                 5.5.3 Euler--Cauchy Differential Equations / 230 \\
                 5.5.4 Variation of Parameters / 232 \\
                 5.6 Mechanical Vibrations / 235 \\
                 5.6.1 Free Vibration / 236 \\
                 5.6.2 Free Vibration with Viscous Damping / 238 \\
                 5.6.3 Free Vibration with Coulomb Damping / 241 \\
                 5.6.4 Forced Vibration without Damping / 244 \\
                 5.6.5 Forced Vibration with Viscous Damping / 247 \\
                 5.7 Electric Circuits / 249 \\
                 5.7.1 Analog Computation / 250 \\
                 5.7.2 Complex Solution and Impedance / 252 \\
                 5.8 Systems of Simultaneous Linear Differential
                 Equations / 254 \\
                 5.8.1 The Reduction of a System to a Single Equation /
                 254 \\
                 5.8.2 Cramer's Rule for Simultaneous Differential
                 Equations / 255 \\
                 5.8.3 Simultaneous Equations as an Eigenvalue Problem /
                 257 \\
                 5.8.4 Transformation of an $n$th Order Equation into a
                 System of $n$ First-Order Equations / 259 \\
                 5.8.5 Coupled Oscillators and Normal Modes / 261 \\
                 5.9 Other Methods and Resources for Differential
                 Equations / 264 \\
                 Exercises / 265 \\
                 6 Laplace Transforms / 271 \\
                 6.1 Definition and Properties of Laplace Transforms /
                 271 \\
                 6.1.1 Laplace Transform --- A Linear Operator / 271 \\
                 6.1.2 Laplace Transforms of Derivatives / 274 \\
                 6.1.3 Substitution: $s$-Shifting / 275 \\
                 6.1.4 Derivative of a Transform / 276 \\
                 6.1.5 A Short Table of Laplace Transforms / 276 \\
                 6.2 Solving Differential Equation with Laplace
                 Transform / 278 \\
                 6.2.1 Inverse Laplace Transform / 278 \\
                 6.2.2 Solving Differential Equations / 288 \\
                 6.3 Laplace Transform of Impulse and Step Functions /
                 291 \\
                 6.3.1 The Dirac Delta Function / 291 \\
                 6.3.2 The Heaviside Unit Step Function / 294 \\
                 6.4 Differential Equations with Discontinuous Forcing
                 Functions / 297 \\
                 6.5 Convolution / 302 \\
                 6.5.1 The Duhamel Integral / 302 \\
                 6.5.2 The Convolution Theorem / 304 \\
                 6.6 Further Properties of Laplace Transforms / 307 \\
                 6.6.1 Transforms of Integrals / 307 \\
                 6.6.2 Integration of Transforms / 307 \\
                 6.6.3 Scaling / 308 \\
                 6.6.4 Laplace Transforms of Periodic Functions / 309
                 \\
                 6.6.5 Inverse Laplace Transforms Involving Periodic
                 Functions / 311 \\
                 6.6.6 Laplace Transforms and Gamma Functions / 312 \\
                 6.7 Summary of Operations of Laplace Transforms / 313
                 \\
                 6.8 Additional Applications of Laplace Transforms / 316
                 \\
                 6.8.1 Evaluating Integrals / 316 \\
                 6.8.2 Differential Equation with Variable Coefficients
                 / 319 \\
                 6.8.3 Integral and Integrodifferential Equations / 321
                 \\
                 6.9 Inversion by Contour Integration / 323 \\
                 6.10 Computer Algebraic Systems for Laplace Transforms
                 / 326 \\
                 Exercises / 328 \\
                 References / 333 \\
                 Index / 335",
}

@Book{Tang:2007:MMEc,
  author =       "Kwong-Tin Tang",
  title =        "Mathematical Methods for Engineers and Scientists: 3.
                 {Fourier} Analysis, Partial Differential Equations and
                 Variational Methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 438",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-3-540-44697-2",
  ISBN =         "3-540-44695-8 (hardcover), 3-540-44697-4 (e-book)",
  ISBN-13 =      "978-3-540-44695-8 (hardcover), 978-3-540-44697-2
                 (e-book)",
  LCCN =         "QA401 .T36 2007",
  bibdate =      "Fri Nov 21 07:29:33 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1936--",
  subject =      "Mathematical physics; Textbooks; Engineering
                 mathematics; Mathematical models",
  tableofcontents = "Part I Fourier Analysis \\
                 1 Fourier Series / 3 \\
                 1.1 Fourier Series of Functions with Periodicity $2
                 \pi$ / 3 \\
                 1.1.1 Orthogonality of Trigonometric Functions / 3 \\
                 1.1.2 The Fourier Coefficients / 5 \\
                 1.1.3 Expansion of Functions in Fourier Series / 6 \\
                 1.2 Convergence of Fourier Series / 9 \\
                 1.2.1 Dirichlet Conditions / 9 \\
                 1.2.2 Fourier Series and Delta Function / 10 \\
                 1.3 Fourier Series of Functions of any Period / 13 \\
                 1.3.1 Change of Interval / 13 \\
                 1.3.2 Fourier Series of Even and Odd Functions / 21 \\
                 1.4 Fourier Series of Nonperiodic Functions in Limited
                 Range / 24 \\
                 1.5 Complex Fourier Series / 29 \\
                 1.6 The Method of Jumps / 32 \\
                 1.7 Properties of Fourier Series / 37 \\
                 1.7.1 Parseval's Theorem / 37 \\
                 1.7.2 Sums of Reciprocal Powers of Integers / 39 \\
                 1.7.3 Integration of Fourier Series / 42 \\
                 1.7.4 Differentiation of Fourier Series / 43 \\
                 1.8 Fourier Series and Differential Equations / 45 \\
                 1.8.1 Differential Equation with Boundary Conditions /
                 45 \\
                 1.8.2 Periodically Driven Oscillator / 49 \\
                 Exercises / 52 \\
                 2 Fourier Transforms / 61 \\
                 2.1 Fourier Integral as a Limit of a Fourier Series /
                 61 \\
                 2.1.1 Fourier Cosine and Sine Integrals / 65 \\
                 2.1.2 Fourier Cosine and Sine Transforms / 67 \\
                 2.2 Tables of Transforms / 72 \\
                 2.3 The Fourier Transform / 72 \\
                 2.4 Fourier Transform and Delta Function / 79 \\
                 2.4.1 Orthogonality / 79 \\
                 2.4.2 Fourier Transforms Involving Delta Functions / 80
                 \\
                 2.4.3 Three-Dimensional Fourier Transform Pair / 81 \\
                 2.5 Some Important Transform Pairs / 85 \\
                 2.5.1 Rectangular Pulse Function / 85 \\
                 2.5.2 Gaussian Function / 85 \\
                 2.5.3 Exponentially Decaying Function / 87 \\
                 2.6 Properties of Fourier Transform / 88 \\
                 2.6.1 Symmetry Property / 88 \\
                 2.6.2 Linearity, Shifting, Scaling / 89 \\
                 2.6.3 Transform of Derivatives / 91 \\
                 2.6.4 Transform of Integral / 92 \\
                 2.6.5 Parseval's Theorem / 92 \\
                 2.7 Convolution / 94 \\
                 2.7.1 Mathematical Operation of Convolution / 94 \\
                 2.7.2 Convolution Theorems / 96 \\
                 2.8 Fourier Transform and Differential Equations / 99
                 \\
                 2.9 The Uncertainty of Waves / 103 \\
                 Exercises / 105 \\
                 Part II Sturm--Liouville Theory and Special Functions
                 \\
                 3 Orthogonal Functions and Sturm--Liouville Problems /
                 111 \\
                 3.1 Functions as Vectors in Infinite Dimensional Vector
                 Space / 111 \\
                 3.1.1 Vector Space / 111 \\
                 3.1.2 Inner Product and Orthogonality / 113 \\
                 3.1.3 Orthogonal Functions / 116 \\
                 3.2 Generalized Fourier Series / 121 \\
                 3.3 Hermitian Operators / 123 \\
                 3.3.1 Adjoint and Self-adjoint (Hermitian) Operators /
                 123 \\
                 3.3.2 Properties of Hermitian Operators / 125 \\
                 3.4 Sturm--Liouville Theory / 130 \\
                 3.4.1 Sturm--Liouville Equations / 130 \\
                 3.4.2 Boundary Conditions of Sturm--Liouville Problems
                 / 132 \\
                 3.4.3 Regular Sturm--Liouville Problems / 133 \\
                 3.4.4 Periodic Sturm--Liouville Problems / 141 \\
                 3.4.5 Singular Sturm--Liouville Problems / 142 \\
                 3.5 Green's Function / 149 \\
                 3.5.1 Green's Function and Inhomogeneous Differential
                 Equation / 149 \\
                 3.5.2 Green's Function and Delta Function / 150 \\
                 Exercises / 157 \\
                 4 Bessel and Legendre Functions / 163 \\
                 4.1 Frobenius Method of Differential Equations / 164
                 \\
                 4.1.1 Power Series Solution of Differential Equation /
                 164 \\
                 4.1.2 Classifying Singular Points / 166 \\
                 4.1.3 Frobenius Series / 167 \\
                 4.2 Bessel Functions / 171 \\
                 4.2.1 Bessel Functions $J_n(x)$ of Integer Order / 172
                 \\
                 4.2.2 Zeros of the Bessel Functions / 174 \\
                 4.2.3 Gamma Function / 175 \\
                 4.2.4 Bessel Function of Noninteger Order / 177 \\
                 4.2.5 Bessel Function of Negative Order / 179 \\
                 4.2.6 Neumann Functions and Hankel Functions / 179 \\
                 4.3 Properties of Bessel Function / 182 \\
                 4.3.1 Recurrence Relations / 182 \\
                 4.3.2 Generating Function of Bessel Functions / 185 \\
                 4.3.3 Integral Representation / 186 \\
                 4.4 Bessel Functions as Eigenfunctions of
                 Sturm--Liouville Problems / 187 \\
                 4.4.1 Boundary Conditions of Bessel's Equation / 187
                 \\
                 4.4.2 Orthogonality of Bessel Functions / 188 \\
                 4.4.3 Normalization of Bessel Functions / 189 \\
                 4.5 Other Kinds of Bessel Functions / 191 \\
                 4.5.1 Modified Bessel Functions / 191 \\
                 4.5.2 Spherical Bessel Functions / 192 \\
                 4.6 Legendre Functions / 196 \\
                 4.6.1 Series Solution of Legendre Equation / 196 \\
                 4.6.2 Legendre Polynomials / 200 \\
                 4.6.3 Legendre Functions of the Second Kind / 202 \\
                 4.7 Properties of Legendre Polynomials / 204 \\
                 4.7.1 Rodrigues' Formula / 204 \\
                 4.7.2 Generating Function of Legendre Polynomials / 206
                 \\
                 4.7.3 Recurrence Relations / 208 \\
                 4.7.4 Orthogonality and Normalization of Legendre
                 Polynomials / 211 \\
                 4.8 Associated Legendre Functions and Spherical
                 Harmonics / 212 \\
                 4.8.1 Associated Legendre Polynomials / 212 \\
                 4.8.2 Orthogonality and Normalization of Associated
                 Legendre Functions / 214 \\
                 4.8.3 Spherical Harmonics / 217 \\
                 4.9 Resources on Special Functions / 218 \\
                 Exercises / 219 \\
                 Part III Partial Differential Equations \\
                 5 Partial Differential Equations in Cartesian
                 Coordinates / 229 \\
                 5.1 One-Dimensional Wave Equations / 230 \\
                 5.1.1 The Governing Equation of a Vibrating String /
                 230 \\
                 5.1.2 Separation of Variables / 232 \\
                 5.1.3 Standing Wave / 238 \\
                 5.1.4 Traveling Wave / 242 \\
                 5.1.5 Nonhomogeneous Wave Equations / 248 \\
                 5.1.6 D'Alembert's Solution of Wave Equations / 252 \\
                 5.2 Two-Dimensional Wave Equations / 261 \\
                 5.2.1 The Governing Equation of a Vibrating Membrane /
                 261 \\
                 5.2.2 Vibration of a Rectangular Membrane / 262 \\
                 5.3 Three-Dimensional Wave Equations / 267 \\
                 5.3.1 Plane Wave / 268 \\
                 5.3.2 Particle Wave in a Rectangular Box / 270 \\
                 5.4 Equation of Heat Conduction / 272 \\
                 5.5 One-Dimensional Diffusion Equations / 274 \\
                 5.5.1 Temperature Distributions with Specified Values
                 at the Boundaries / 275 \\
                 5.5.2 Problems Involving Insulated Boundaries / 278 \\
                 5.5.3 Heat Exchange at the Boundary / 280 \\
                 5.6 Two-Dimensional Diffusion Equations: Heat Transfer
                 in a Rectangular Plate / 284 \\
                 5.7 Laplace's Equations / 286 \\
                 5.7.1 Two-Dimensional Laplace's Equation: Steady-State
                 Temperature in a Rectangular Plate / 287 \\
                 5.7.2 Three-Dimensional Laplace's Equation:
                 Steady-State Temperature in a Rectangular
                 Parallelepiped / 289 \\
                 5.8 Helmholtz's Equations / 291 \\
                 Exercises / 292 \\
                 6 Partial Differential Equations with Curved Boundaries
                 / 301 \\
                 6.1 The Laplacian / 302 \\
                 6.2 Two-Dimensional Laplace's Equations / 304 \\
                 6.2.1 Laplace's Equation in Polar Coordinates / 304 \\
                 6.2.2 Poisson's Integral Formula / 312 \\
                 6.3 Two-Dimensional Helmholtz's Equations in Polar
                 Coordinates / 315 \\
                 6.3.1 Vibration of a Drumhead: Two Dimensional Wave
                 Equation in Polar Coordinates / 316 \\
                 6.3.2 Heat Conduction in a Disk: Two Dimensional
                 Diffusion Equation in Polar Coordinates / 322 \\
                 6.3.3 Laplace's Equations in Cylindrical Coordinates /
                 326 \\
                 6.3.4 Helmholtz's Equations in Cylindrical Coordinates
                 / 331 \\
                 6.4 Three-Dimensional Laplacian in Spherical
                 Coordinates / 334 \\
                 6.4.1 Laplace's Equations in Spherical Coordinates /
                 334 \\
                 6.4.2 Helmholtz's Equations in Spherical Coordinates /
                 345 \\
                 6.4.3 Wave Equations in Spherical Coordinates / 346 \\
                 6.5 Poisson's Equations / 349 \\
                 6.5.1 Poisson's Equation and Green's Function / 351 \\
                 6.5.2 Green's Function for Boundary Value Problems /
                 355 \\
                 Exercises / 359 \\
                 Part IV Variational Methods \\
                 7 Calculus of Variation / 367 \\
                 7.1 The Euler--Lagrange Equation / 368 \\
                 7.1.1 Stationary Value of a Functional / 368 \\
                 7.1.2 Fundamental Theorem of Variational Calculus / 370
                 \\
                 7.1.3 Variational Notation / 372 \\
                 7.1.4 Special Cases / 373 \\
                 7.2 Constrained Variation / 377 \\
                 7.3 Solutions to Some Famous Problems / 380 \\
                 7.3.1 The Brachistochrone Problem / 380 \\
                 7.3.2 Isoperimetric Problems / 384 \\
                 7.3.3 The Catenary / 386 \\
                 7.3.4 Minimum Surface of Revolution / 391 \\
                 7.3.5 Fermat's Principle / 394 \\
                 7.4 Some Extensions / 397 \\
                 7.4.1 Functionals with Higher Derivatives / 397 \\
                 7.4.2 Several Dependent Variables / 399 \\
                 7.4.3 Several Independent Variables / 401 \\
                 7.5 Sturm--Liouville Problems and Variational
                 Principles / 403 \\
                 7.5.1 Variational Formulation of Sturm--Liouville
                 Problems / 403 \\
                 7.5.2 Variational Calculations of Eigenvalues and
                 Eigenfunctions / 405 \\
                 7.6 Rayleigh--Ritz Methods for Partial Differential
                 Equations / 410 \\
                 7.6.1 Laplace's Equation / 411 \\
                 7.6.2 Poisson's Equation / 415 \\
                 7.6.3 Helmholtz's Equation / 417 \\
                 7.7 Hamilton's Principle / 420 \\
                 Exercises / 425 \\
                 References / 431 \\
                 Index / 433",
}

@Book{Turnbull:1932:ITC,
  author =       "Herbert Westren Turnbull and Alexander Craig Aitken",
  title =        "An Introduction to the Theory of Canonical Matrices",
  publisher =    pub-BLACKIE,
  address =      pub-BLACKIE:adr,
  pages =        "192",
  year =         "1932",
  LCCN =         "QA263 .T8",
  MRclass =      "15.30",
  MRnumber =     "0123581 (23 \#A906)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "H. W. Turnbull (1885--1961); A. C. Aitken
                 (1895--1967)",
}

@Book{Turnbull:1950:TDM,
  author =       "H. W. (Herbert Westren) Turnbull",
  title =        "Theory of Determinants, Matrices and Invariants",
  publisher =    pub-BLACKIE,
  address =      pub-BLACKIE:adr,
  edition =      "Second",
  pages =        "xvi + 368",
  year =         "1950",
  LCCN =         "????",
  bibdate =      "Fri Nov 21 12:17:51 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Turnbull:1952:ITC,
  author =       "Herbert Westren Turnbull and Alexander Craig Aitken",
  title =        "An Introduction to the Theory of Canonical Matrices",
  publisher =    pub-BLACKIE,
  address =      pub-BLACKIE:adr,
  edition =      "Second",
  pages =        "xiii + 200",
  year =         "1952",
  LCCN =         "????",
  MRclass =      "15.30",
  MRnumber =     "0123581 (23 \#A906)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "H. W. Turnbull (1885--1961); A. C. Aitken
                 (1895--1967)",
}

@Book{Turnbull:1961:ITC,
  author =       "H. W. Turnbull and A. C. Aitken",
  title =        "An Introduction to the Theory of Canonical Matrices",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Third",
  pages =        "xiii + 200",
  year =         "1961",
  LCCN =         "QA263 .T8 1961",
  MRclass =      "15.30",
  MRnumber =     "0123581 (23 \#A906)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Reprint of \cite {Turnbull:1952:ITC}.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Turnbull:2005:ITC,
  author =       "H. W. (Herbert Westren) Turnbull and A. C. (Alexander
                 Craig) Aitken",
  title =        "Introduction to the Theory of Canonical Matrices",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xiii + 200",
  year =         "2005",
  ISBN =         "0-486-44168-7",
  ISBN-13 =      "978-0-486-44168-9",
  LCCN =         "QA263 .T8 2005",
  bibdate =      "Sun Nov 23 11:13:37 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0619/2004061766-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1318/2004061766-t.html",
  acknowledgement = ack-nhfb,
  author-dates = "1885--1961",
  remark =       "This Dover edition, first published in 1961, and
                 reissued in 2005, is an unabridged and corrected
                 republication of the third (1952) edition of the work
                 first published by Blackie and Son Limited, London and
                 Glasgow, in 1932.",
  subject =      "Matrices; Transformations (Mathematics)",
  tableofcontents = "I. Definitions and Fundamental Properties of
                 Matrices \\
                 II. Elementary Transformations. Bilinear and Quadratic
                 Forms \\
                 III. The Canonical Reduction of Equivalent Matrices \\
                 IV. Subgroups of the Group of Equivalent
                 Transformations \\
                 V. A Rational Canonical Form for the Collineatory Group
                 \\
                 VI. The Classical Canonical Form for the Collineatory
                 Group \\
                 VII. Congruent and Conjunctive Transformations:
                 Quadratic and Hermitian Forms \\
                 VIII. Canonical Reductions by Unitary and Orthogonal
                 Transformations \\
                 IX. The Canonical Reduction of Pencils of Matrices \\
                 X. Applications of Canonical Forms to Solution of
                 Linear Matrix Equations. Commutants and Invariants \\
                 XI. Practical Applications of Canonical Reduction \\
                 Appendix \\
                 Miscellaneous Examples \\
                 Index",
}

@Book{Valentine:1964:CS,
  author =       "Frederick A. Valentine",
  title =        "Convex Sets",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "ix + 238",
  year =         "1964",
  LCCN =         "QA248 .V3",
  MRclass =      "52.00",
  MRnumber =     "0170264 (30 \#503)",
  MRreviewer =   "P. C. Hammer",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "McGraw-Hill Series in Higher Mathematics",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Valentine:1976:CS,
  author =       "Frederick A. (Frederick Albert) Valentine",
  title =        "Convex Sets",
  publisher =    pub-R-E-KRIEGER,
  address =      pub-R-E-KRIEGER:adr,
  pages =        "ix + 238",
  year =         "1976",
  ISBN =         "0-88275-289-8",
  ISBN-13 =      "978-0-88275-289-1",
  LCCN =         "QA640 .V34 1975",
  bibdate =      "Sun Nov 23 11:17:06 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1911--",
  remark =       "Reprint of the edition published in the McGraw-Hill
                 Series in Higher Mathematics.",
  subject =      "Convex sets",
}

@Book{Varga:2000:MIA,
  author =       "Richard S. Varga",
  title =        "Matrix Iterative Analysis",
  volume =       "27",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "x + 358",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-3-642-05156-2",
  ISBN =         "3-642-05154-5 (paperback), 3-540-66321-5 (hardcover),
                 3-642-05156-1 (e-book)",
  ISBN-13 =      "978-3-642-05154-8 (paperback), 978-3-540-66321-8
                 (hardcover), 978-3-642-05156-2 (e-book)",
  LCCN =         "QA297.8 .V37 2000",
  MRclass =      "65-01 (15A48 65Fxx)",
  MRnumber =     "1753713 (2001g:65002)",
  MRreviewer =   "George D. Poole",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Springer Series in Computational Mathematics",
  URL =          "http://lcweb.loc.gov/catdir/toc/99050196.html;
                 http://www.loc.gov/catdir/enhancements/fy0815/99050196-d.html;
                 http://www.springerlink.com/openurl.asp?genre=book&isbn=978-3-642-05161-6",
  abstract =     "This book is a revised version of the first edition,
                 originally published by Prentice Hall in 1962 and
                 regarded as a classic in its field. In some places,
                 newer research results, e.g., results on weak regular
                 splittings, have been incorporated in the revision, and
                 in other places, new material has been added in the
                 chapters, as well as at the end of chapters, in the
                 form of additional up-to-date references and some
                 recent theorems to give the reader some newer
                 directions to pursue. The material in the new chapters
                 is basically self-contained and more exercises have
                 been provided for the readers. While the original
                 version was more linear algebra oriented, the revision
                 attempts to emphasize tools from other areas, such as
                 approximation theory and conformal mapping theory, to
                 access newer results of interest. The book should be of
                 great interest to researchers and graduate students in
                 the field of numerical analysis.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "1. Matrix Properties and Concepts / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 A Simple Example / 3 \\
                 1.3 Norms and Spectral Radii / 7 \\
                 1.4 Bounds for the Spectral Radius. of a Matrix and
                 Directed Graphs / 16 \\
                 1.5 Diagonally Dominant Matrices / 22 \\
                 1.6 Ovals of Cassini / 24 \\
                 2. Nonnegative Matrices / 31 \\
                 2.1 Spectral Radii of Nonnegative Matrices / 31 \\
                 2.2 Cyclic and Primitive Matrices / 40 \\
                 2.3 Reducible Matrices / 50 \\
                 2.4 Nonnegative Matrices and Directed Graphs / 53 \\
                 3 Basic Iterative Methods and Comparison Theorems / 63
                 \\
                 3.1 The Point Jacobi, Gauss--Seidel, and Successive
                 Overrelaxation Iterative Methods / 63 \\
                 3.2 Average Rates of Convergence / 68 \\
                 3.3 The Stein--Rosenberg Theorem / 74 \\
                 3.4 The Ostrowski--Reich Theorem / 81 \\
                 3.5 Stieltjes Matrices, $M$-Matrices and $H$-Matrices /
                 87 \\
                 3.6 Regular and Weak Regular Splittings of Matrices /
                 94 \\
                 4. Successive Overrelaxation Iterative Methods / 111
                 \\
                 4.1 $p$-Cyclic Matrices / 111 \\
                 4.2 The Successive Overrelaxation Iterative Method for
                 $p$-Cyclic Matrices / 119 \\
                 4.3 Theoretical Determination of an Optimum Relaxation
                 Factor / 123 \\
                 4.4 Extensions of the $2$-Cyclic Theory of Matrices /
                 130 \\
                 4.5 Asymptotic Rates of Convergence / 141 \\
                 4.6 CO$(q,r)$ and GCO$(q,r)$: Generalized Consistent
                 Orderings / 143 \\
                 5. Semi-Iterative Methods / 149 \\
                 5.1 Semi-Iterative Methods and Chebyshev Polynomials /
                 149 \\
                 5.2 Relationship of Semi-Iterative Methods to
                 Successive Overrelaxation Iterative Methods / 158 \\
                 5.3 Comparison of Average Rates of Convergence: the
                 Weakly Cyclic Case / 165 \\
                 5.4 Cyclic Reduction and Related Iterative Methods /
                 170 \\
                 5.5 Semi-Iterative Methods Applied to the Successive
                 Overrelaxation Method / 174 \\
                 6. Derivation and Solution of Elliptic Difference
                 Equations / 183 \\
                 6.1 A Simple Two-Point Boundary-Value Problem / 183 \\
                 6.2 General Second-Order Ordinary Differential
                 Equations / 196 \\
                 6.3 Derivation of Finite Difference Approximations in
                 Higher Dimensions / 204 \\
                 6.4 Factorization Techniques and Block Iterative
                 Methods / 219 \\
                 6.5 Asymptotic Convergence Rates for the Model Problem
                 / 226 \\
                 7. Alternating-Direction Implicit Iterative Methods /
                 235 \\
                 7.1 The Peaceman--Rachford Iterative Method / 235 \\
                 7.2 The Commutative Case / 245 \\
                 7.3 The Noncommutative Case / 255 \\
                 7.4 Variants of the Peaceman--Rachford Iterative Method
                 / 264 \\
                 8. Matrix Methods for Parabolic Partial Differential
                 Equations / 275 \\
                 8.1 Semi-Discrete Approximation / 275 \\
                 8.2 Essentially Positive Matrices / 281 \\
                 8.3 Matrix Approximations for $\exp(-t S)$ / 287 \\
                 8.4 Relationship with Iterative Methods for Solving
                 Elliptic Difference Equations / 296 \\
                 8.5 Chebyshev Rational Approximations for $\exp(-t S)$
                 / 304 \\
                 9. Estimation of Acceleration Parameters / 313 \\
                 9.1 Application of the Theory of Nonnegative Matrices /
                 313 \\
                 9.2 Application of Isoperimetric Inequalities / 321 \\
                 A. Appendix / 329 \\
                 B. Appendix / 333 \\
                 References / 337 \\
                 Index / 355",
}

@Book{Varga:2004:GHC,
  author =       "Richard S. Varga",
  title =        "{Ger{\v{s}}gorin} and His Circles",
  volume =       "36",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 226",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-3-642-17798-9",
  ISBN =         "3-540-21100-4 (hardcover), 3-642-17798-0 (e-book)",
  ISBN-13 =      "978-3-540-21100-6 (hardcover), 978-3-642-17798-9
                 (e-book)",
  ISSN =         "0179-3632",
  ISSN-L =       "0179-3632",
  LCCN =         "QA193 .V37 2004",
  MRclass =      "15-02 (15-03 15A18 15A42 65-02 65-03 65F15)",
  MRnumber =     "2093409 (2005h:15002)",
  MRreviewer =   "David Scott Watkins",
  bibdate =      "Sun Mar 25 09:35:13 MDT 2018",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/t/taussky-todd-olga.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Springer Series in Computational Mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0815/2004104814-d.html",
  abstract =     "This book studies the original results, and their
                 extensions, of the Russian mathematician, S. A.
                 Ger{\v{s}}gorin, who wrote a seminal paper in 1931, on
                 how to easily obtain estimates of all $n$ eigenvalues
                 (characteristic values) of any given $n$-by-$n$ complex
                 matrix. Since the publication of this paper, there has
                 been many newer results spawned by his paper, and this
                 book will be the first which is devoted solely to this
                 resulting area. As such, it will include the latest
                 research results, such as Brauer ovals of Cassini and
                 Brualdi lemniscates, and their comparisons. This book
                 is dedicated to the late Olga Taussky-Todd and her
                 husband, John Todd. It was Olga who brought to light
                 Ger{\v{s}}gorin's paper and its significance to the
                 mathematical world. The level of this book requires
                 only a modest background in linear algebra and
                 analysis, and is therefore comprehensible to
                 upper-level and graduate level students in
                 mathematics.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "Richard S. Varga (8 October 1928--25 February 2022)",
  shorttableofcontents = "I. Preface / vii \\
                 1. Basic theory / 1 \\
                 2. Ger{\v{s}}gorian-type eigenvalue inclusion theorems
                 / 35 \\
                 3. More eigenvalue inclusion results / 73 \\
                 4. Minimal Ger{\v{s}}gorian sets and their sharpness /
                 97 \\
                 5. G-functions / 127 \\
                 6. Ger{\v{s}}gorian-type theorems for partitioned
                 matrices / 155 \\
                 Appendices: / \\
                 A. Ger{\v{s}}gorin's paper from 1931, and comments /
                 189 \\
                 B. Vector norms and induced operator norms / 199 \\
                 C. The Perron--Frobenius theory of nonnegative matrices
                 / 201 \\
                 D. Matlab 6 programs / 205 \\
                 References / 217",
  subject =      "Ger{\v{s}}gorin, Semen Aronovich; Algebras, Linear;
                 Eigenvalues; Valeurs propres; Alg{\`e}bre lin{\'e}aire;
                 Eigenvalues; Algebras, Linear; Komplexe Matrix;
                 Matrizen-Eigenwertaufgabe",
  subject-dates = "Semen Aronovich Ger{\v{s}}gorin (1901--1933)",
  tableofcontents = "I. Preface / vii \\
                 1. Basic Theory / 1 \\
                 1.1 Ger{\v{s}}gorin's Theorem / 1 \\
                 1.2 Extensions of Ger{\v{s}}gorin's Theorem via Graph
                 Theory / 10 \\
                 1.3 Analysis Extensions of Ger{\v{s}}gorin's Theorem
                 and Fan's Theorem / 18 \\
                 1.4 A Norm Derivation of Ger{\v{s}}gorin's Theorem 1.1
                 / 26 \\
                 2. Ger{\v{s}}gorin-Type Eigenvalue Inclusion Theorems /
                 35 \\
                 2.1 Brauer's Ovals of Cassini / 35 \\
                 2.2 Higher-Order Lemniscates / 43 \\
                 2.3 Comparison of the Brauer Sets and the Brualdi Sets
                 / 53 \\
                 2.4 The Sharpness of Brualdi Lemniscate Sets / 58 \\
                 2.5 An Example / 67 \\
                 3. More Eigenvalue Inclusion Results / 73 \\
                 3.1 The Parodi--Schneider Eigenvalue Inclusion Sets /
                 73 \\
                 3.2 The Field of Values of a Matrix / 79 \\
                 3.3 Newer Eigenvalue Inclusion Sets / 84 \\
                 3.4 The Pupkov--Solov'ev Eigenvalue Inclusions Set / 92
                 \\
                 4. Minimal Ger{\v{s}}gorin Sets and Their Sharpness /
                 97 \\
                 4.1 Minimal Ger{\v{s}}gorin Sets / 97 \\
                 4.2 Minimal Ger{\v{s}}gorin Sets via Permutations / 110
                 \\
                 4.3 A Comparison of Minimal Ger{\v{s}}gorin Sets and
                 Brualdi Sets / 121 \\
                 5. $G$-Functions / 127 \\
                 5.1 The Sets ${\cal F}_n$ and ${\cal G}_n$ / 127 \\
                 5.2 Structural Properties of ${\cal G}_n$ and ${\cal
                 G}_n^c$ / 133 \\
                 5.3 Minimal $G$-Functions / 141 \\
                 5.4 Minimal $G$-Functions with Small Domains of
                 Dependence / 145 \\
                 5.5 Connections with Brauer Sets and Generalized
                 Brualdi Sets / 149 \\
                 6. Ger{\v{s}}gorin-Type Theorems for Partitioned
                 Matrices / 155 \\
                 6.1 Partitioned Matrices and Block Diagonal Dominance /
                 155 \\
                 6.2 A Different Norm Approach / 164 \\
                 6.3 A Variation on a Theme by Brualdi / 174 \\
                 6.4 $G$-Functions in the Partitioned Case / 181 \\
                 Appendix A. Ger{\v{s}}gorin's Paper from 1931, and
                 Comments / 189 \\
                 Appendix B. Vector Norms and Induced Operator Norms /
                 199 \\
                 Appendix C. The Perron--Frobenius Theory of Nonnegative
                 Matrices / 201 \\
                 Appendix D. Matlab 6 Programs / 205 \\
                 References / 217",
}

@Book{Wedderburn:1934:LM,
  author =       "J. H. M. (Joseph Henry Maclagan) Wedderburn",
  title =        "Lectures on Matrices",
  volume =       "XVII",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "vii + 200",
  year =         "1934",
  LCCN =         "QA1 .A5225 vol. 17a",
  bibdate =      "Fri Nov 21 12:27:23 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "American Mathematical Society. Colloquium
                 publications",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1882--1948",
  remark =       "This book contains lectures on matrices given at
                 Princeton university at various times since 1926.",
}

@Book{Wedderburn:1964:LM,
  author =       "J. H. M. (Joseph Henry Maclagan) Wedderburn",
  title =        "Lectures on Matrices",
  volume =       "XVII",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "vii + 200",
  year =         "1964",
  LCCN =         "QA1 .A5225 vol. 17a",
  MRclass =      "15.00 (01.60)",
  MRnumber =     "0168568 (29 \#5828)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "American Mathematical Society. Colloquium
                 publications",
  acknowledgement = ack-nhfb,
  remark =       "Reprint of \cite{Wedderburn:1934:LM}.",
}

@Book{Wedderburn:2005:LM,
  author =       "J. H. M. (Joseph Henry Maclagan) Wedderburn",
  title =        "Lectures on Matrices",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "vii + 200",
  year =         "2005",
  ISBN =         "0-486-44167-9",
  ISBN-13 =      "978-0-486-44167-2",
  LCCN =         "QA188 .W43 2005",
  bibdate =      "Fri Nov 21 12:27:23 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Dover phoenix editions",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0618/2004059120-d.html",
  abstract =     "This definitive presentation of matrix theory is the
                 work of one of America's most significant contributors
                 to this area. The first three chapters take matrix
                 theory up to elementary divisors, proceeding to
                 examinations of vector polynomials and singular matric
                 polynomials. A discussion of compound matrices follows,
                 succeeded by considerations of Hermitian, symmetric,
                 and skew matrices, with a number of interesting proofs
                 of properties. Subsequent chapters are devoted to
                 commutative matrices, matrix functions, and the
                 automorphic transformation of a bilinear form. The
                 final chapter offers a masterly handling of linear
                 associative algebras.",
  acknowledgement = ack-nhfb,
  author-dates = "1882--1948",
  remark =       "Reprint of \cite{Wedderburn:1934:LM}.",
  subject =      "Matrices",
}

@Book{Wielandt:1967:TAT,
  author =       "Helmut W. Wielandt and Robert R. Meyer",
  title =        "Topics in the Analytic Theory of Matrices: Lecture
                 Notes",
  publisher =    "Department of Mathematics, University of Wisconsin",
  address =      "Madison, WI, USA",
  pages =        "129",
  year =         "1967",
  LCCN =         "QA262 .F72; QA263 .W43",
  bibdate =      "Fri Nov 21 12:30:23 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Reprinted in \cite[271--352]{Huppert:1996:HWM}.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  remark =       "Lecture notes prepared by Robert R. Meyer and from a
                 course by Helmut Wielandt [at the University of
                 Wisconsin in Madison during the second semester
                 1966/67].",
}

@Book{Wilkinson:1965:AEP,
  author =       "J. H. Wilkinson",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xviii + 662",
  year =         "1965",
  LCCN =         "QA218 .W5",
  MRclass =      "65.40",
  MRnumber =     "0184422 (32 \#1894)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
}

@Book{Wilkinson:1988:AEP,
  author =       "J. H. Wilkinson",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xviii + 662",
  year =         "1988",
  ISBN =         "0-19-853418-3",
  ISBN-13 =      "978-0-19-853418-1",
  LCCN =         "QA218 .W5 1988",
  MRclass =      "65Fxx (15-02 65-02)",
  MRnumber =     "MR950175 (89j:65031)",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Oxford Science Publications",
  series =       "Monographs on Numerical Analysis",
  URL =          "http://www.gbv.de/dms/bowker/toc/9780198534181.pdf;
                 http://www.loc.gov/catdir/enhancements/fy0604/87028274-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0604/87028274-t.html",
  abstract =     "This volume, which became a classic on first
                 publication, is perhaps the most important and widely
                 read book in the field of numerical analysis. It
                 presents a distillation of the author's pioneering
                 discoveries concerning the computation of matrix
                 eigenvalues. The emphasis is on the transmission of
                 knowledge rather than elaborate proofs. The book will
                 be valued by all practising numerical analysts,
                 students and researchers in the field, engineers, and
                 scientists.",
  tableofcontents = "1. Theoretical Background \\
                 2. Perturbation Theory \\
                 3. Error Analysis \\
                 4. Solution of Linear Algebraic Equations \\
                 5. Hermitian Matrices \\
                 6. Reduction of a General Matrix to Condensed Form \\
                 7. Eigenvalues of Matrices of Condensed Forms \\
                 8. The $L R$ and $Q R$ Algorithms \\
                 9. Iterative Methods \\
                 Bibliography \\
                 Index",
}

@Book{Zhan:2002:MI,
  author =       "Xingzhi Zhan",
  title =        "Matrix Inequalities",
  volume =       "1790",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 116",
  year =         "2002",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/b83956",
  ISBN =         "3-540-43798-3 (print), 3-540-45421-7 (e-book)",
  ISBN-13 =      "978-3-540-43798-7 (print), 978-3-540-45421-2
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  LCCN =         "QA3 .L28 no. 1790",
  MRclass =      "15A45 (15-02; 15A15; 15A18; 15A42; 15A60; 15A48;
                 26D15; 15A51); 15A45 (47A30 47A63)",
  MRnumber =     "1927396 (2003h:15030)",
  MRreviewer =   "T. Ando",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm2000.bib",
  series =       ser-LECT-NOTES-MATH,
  URL =          "http://link.springer.com/book/10.1007/b83956;
                 http://www.loc.gov/catdir/enhancements/fy0817/2002070800-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0817/2002070800-t.html;
                 http://www.springerlink.com/content/978-3-540-45421-2;
                 http://www.springerlink.com/openurl.asp?genre=issue&issn=0075-8434&volume=1790",
  ZMnumber =     "1018.15016",
  abstract =     "The main purpose of this monograph is to report on
                 recent developments in the field of matrix
                 inequalities, with emphasis on useful techniques and
                 ingenious ideas. Among other results this book contains
                 the affirmative solutions of eight conjectures. Many
                 theorems unify or sharpen previous inequalities. The
                 author's aim is to streamline the ideas in the
                 literature. The book can be read by research workers,
                 graduate students and advanced undergraduates.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  fseries =      "Lecture Notes in Mathematics",
  series-URL =   "http://link.springer.com/bookseries/304",
  tableofcontents = "1. Inequalities in the L{\"o}wner Partial Order \\
                 1.1 The L{\"o}wner--Heinz inequality \\
                 1.2 Maps on matrix spaces \\
                 1.3 Inequalities for matrix powers \\
                 1.4 Block matrix techniques \\
                 2. Majorization and Eigenvalues \\
                 2.1 Majorizations \\
                 2.2 Eigenvalues of Hadamard products \\
                 3. Singular Values \\
                 3.1 Matrix Young inequalities \\
                 3.2 Singular values of Hadamard products \\
                 3.3 Differences of positive semidefinite matrices \\
                 3.4 Matrix Cartesian decompositions \\
                 3.5 Singular values and matrix entries \\
                 4. Norm Inequalities \\
                 4.1 Operator monotone functions \\
                 4.2 Cartesian decompositions revisited \\
                 4.3 Arithmetic-geometric mean inequalities \\
                 4.4 Inequalities of Holder and Minkowski types \\
                 4.5 Permutations of matrix entries \\
                 4.6 The numerical radius \\
                 4.7 Norm estimates of banded matrices \\
                 5. Solution of the van der Waerden Conjecture",
}

@Book{Zhang:2009:LAC,
  author =       "Fuzhen Zhang",
  title =        "Linear Algebra: Challenging Problems for Students",
  publisher =    pub-JOHNS-HOPKINS,
  address =      pub-JOHNS-HOPKINS:adr,
  edition =      "Second",
  pages =        "xviii + 245",
  year =         "2009",
  ISBN =         "0-8018-9125-6 (hardcover), 0-8018-9126-4 (paperback)",
  ISBN-13 =      "978-0-8018-9125-0 (hardcover), 978-0-8018-9126-7
                 (paperback)",
  LCCN =         "QA184.5 .Z48 2009",
  MRclass =      "15-01",
  MRnumber =     "2501859 (2010b:15001)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Johns Hopkins Studies in the Mathematical Sciences",
  abstract =     "Linear algebra is a prerequisite for students majoring
                 in mathematics and is required of many undergraduate
                 and first-year graduate students in statistics,
                 engineering, and related areas. This fully updated and
                 revised text defines the discipline's main terms,
                 explains its key theorems, and provides over 425
                 example problems ranging from the elementary to some
                 that may baffle even the most seasoned mathematicians.
                 Vital concepts are highlighted at the beginning of each
                 chapter and a final section contains hints for solving
                 the problems as well as solutions to each example.
                 Based on Fuzhen Zhang's experience teaching and
                 researching algebra over the past two decades,
                 \booktitle{Linear Algebra} is the perfect examination
                 study tool. Students in beginning and seminar-type
                 advanced linear algebra classes and those seeking to
                 brush up on the topic will find Zhang's plain
                 discussions of the subject's theories refreshing and
                 the problems diverse, interesting, and challenging.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "1961--",
  subject =      "Algebras, Linear; Problems, exercises, etc",
  tableofcontents = "Preface / ix \\
                 Vector spaces / 1\\
                 Determinants, inverses and rank of matrices, and
                 systems of linear equations / 9 \\
                 Matrix similarity, eigenvalues, eigenvectors, and
                 linear transformations / 23 \\
                 Special matrices / 41 \\
                 Inner product spaces / 61 \\
                 Hints and Solutions / 71 \\
                 Main References / 169 \\
                 Notation / 171 \\
                 Index / 173",
}

@Book{Zhang:2011:MTB,
  author =       "Fuzhen Zhang",
  title =        "Matrix Theory: Basic Results and Techniques",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xviii + 399",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-1-4614-1099-7",
  ISBN =         "1-4614-1098-3 (paperback), 1-4614-1099-1 (e-book)",
  ISBN-13 =      "978-1-4614-1098-0 (paperback), 978-1-4614-1099-7
                 (e-book)",
  LCCN =         "QA188 .Z47 2011",
  MRclass =      "15-02 (15A09 15A15 15A18 15A45 15A54 15A60)",
  MRnumber =     "2857760 (2012h:15001)",
  MRreviewer =   "Mohammad Sal Moslehian",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Universitext",
  URL =          "http://www.loc.gov/catdir/enhancements/fy1406/2011935372-b.html;
                 http://www.loc.gov/catdir/enhancements/fy1406/2011935372-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1406/2011935372-t.html",
  abstract =     "The aim of this book is to concisely present
                 fundamental ideas, results, and techniques in linear
                 algebra and mainly matrix theory. The book contains ten
                 chapters covering various topics ranging from
                 similarity and special types of matrices to Schur
                 complements and matrix normality. This book can be used
                 as a textbook or a supplement for a linear algebra and
                 matrix theory class or a seminar for senior
                 undergraduate or graduate students. The book can also
                 serve as a reference for instructors and researchers in
                 the fields of algebra, matrix analysis, operator
                 theory, statistics, computer science, engineering,
                 operations research, economics, and other fields.

                 Major changes in this revised and expanded second
                 edition: * Expansion of topics such as matrix
                 functions, nonnegative matrices, and (unitarily
                 invariant) matrix norms; * A new chapter, Chapter 4,
                 with updated material on numerical ranges and radii,
                 matrix norms, and special operations such as the
                 Kronecker and Hadamard products and compound matrices;
                 * A new chapter, Chapter 10, on matrix inequalities,
                 which presents a variety of inequalities on the
                 eigenvalues and singular values of matrices and
                 unitarily invariant norms.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface to the Second Edition \\
                 Preface \\
                 Frequently Used Notation and Terminology \\
                 Frequently Used Terms \\
                 1 Elementary Linear Algebra Review \\
                 2 Partitioned Matrices, Rank, and Eigenvalues \\
                 3 Matrix Polynomials and Canonical Forms \\
                 4 Numerical Ranges, Matrix Norms, and Special
                 Operations \\
                 5 Special Types of Matrices \\
                 6 Unitary Matrices and Contractions \\
                 7 Positive Semidefinite Matrices \\
                 8 Hermitian Matrices \\
                 9 Normal Matrices \\
                 10 Majorization and Matrix Inequalities \\
                 References \\
                 Notation \\
                 Index",
}

@Book{Zurmuhl:1950:MDI,
  author =       "Rudolf Zurm{\"u}hl",
  title =        "{Matrizen: Eine Darstellung f{\"u}r Ingenieure}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 427",
  year =         "1950",
  ISBN =         "3-642-53289-6",
  ISBN-13 =      "978-3-642-53289-4",
  LCCN =         "QA263 .Z8",
  bibdate =      "Sun Nov 23 13:39:47 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  URL =          "http://d-nb.info/1033262757/34;
                 http://www.springerlink.com/content/978-3-642-53289-4",
  acknowledgement = ack-nhfb,
  author-dates = "1904--1966",
  language =     "German",
  subject =      "Matrices; Matrices; Matrius (Matem{\`a}tica);
                 Matrices; Matrices; Matrices; Matrix (Mathematik);
                 Matrizenrechnung.",
  tableofcontents = "1. Einleitung / 1 \\
                 I. Kapitel. Der Matrizenkalk{\"u}l \\
                 2. Grundbegriffe und einfache Rechenregeln \\
                 2.1. Definitionen und Rechenregeln / 5 \\
                 2.2. Transponierte, symmetrische und schiefsymmetrische
                 Matrix / 8 \\
                 2.3. Diagonalmatrix, Skalarmatrix und Einheitsmatrix /
                 10 \\
                 2.4. Determinanten, singul{\"a}re Matrizen und Rang /
                 11 \\
                 3. Matrizen und Vektoren \\
                 3.1. Vektoren / 13 \\
                 3.2. Spalten- und Zeilenvektoren einer Matrix / 14 \\
                 3.3. Das skalare Produkt / 16 \\
                 3.4. Betrag, Normierung und Orthogonalit{\"a}t / 17 \\
                 4. Matrizenmultiplikation \\
                 4.1. Zusammengesetzte Transformation und
                 Matrizenprodukt / 18 \\
                 4.2. Produkt aus Matrix und Vektor / 23 \\
                 4.3. S{\"a}tze {\"u}ber Matrizenmultiplikation / 24 \\
                 4.4. Multiplikation mit Diagonalmatrizen / 28 \\
                 4.5. Potenzen und Polynome / 29 \\
                 4.6. Das Produkt $\mathfrak{A}' \mathfrak{A}$ / 29 \\
                 4.7. Dyadisches Produkt / 30 \\
                 4.8. Skalares Matrizenprodukt / 32 \\
                 5. Kehrmatrix und Matrizendivision \\
                 5.1. Erkl{\"a}rung und Herleitung der Kehrmatrix / 32
                 \\
                 5.2. Formelm{\"a}{\ss}iger Ausdruck der $\alpha_{i k}$
                 / 36 \\
                 5.3. Einfache Rechenregeln / 38 \\
                 5.4. Matrizendivision / 39 \\
                 6. Lineare Transformationen \\
                 6.1. Geometrische Deutung / 40 \\
                 6.2. Umkehrbarkeit / 42 \\
                 6.3. Koordinatentransformation / 44 \\
                 6.4. Zusammengesetzte Transformationen / 46 \\
                 6.5. Ein Beispiel / 48 \\
                 7. Orthogonale Transformation \\
                 7.1. Eigenschaften orthogonaler Matrizen und
                 Transformationen / 50 \\
                 7.2. Orthogonaldeterminante. Eigentliche und
                 uneigentliche Orthogonaltransformation / 54 \\
                 7.3. Darstellung komplexer Zahlen. Verallgemeinerung
                 der Drehstreckung / 55 \\
                 7.4. Ein Beispiel: Die Eulerschen Winkel / 56 \\
                 II. Kapitel. Der Rang \\
                 8. Determinanten \\
                 8.1. Definitionen / 58 \\
                 8.2. Entwicklung nach Unterdeterminanten / 59 \\
                 8.3. Weitere Determinantens{\"a}tze / 62 \\
                 8.4. Determinantenabsch{\"a}tzung von Hadamard / 64 \\
                 9. Lineare Abh{\"a}ngigkeit und Rang \\
                 9.1. Lineare Abh{\"a}ngigkeit und Rang eines
                 Vektorsystems / 66 \\
                 9.2. Determinantenerkl{\"a}rung des Ranges / 69 \\
                 9.3. Lineare Vektorgebilde / 72 \\
                 9.4. Lineare Abh{\"a}ngigkeit von Funktionen / 73 \\
                 10. Theorie der linearen Gleichungen \\
                 10.1. Der Regelfall. Cramersche Regel / 74 \\
                 10.2. Allgemeine homogene Gleichungssysteme / 78 \\
                 10.3. Allgemeine inhomogene Gleichungssysteme / 85 \\
                 11. {\"A}quivalenz und Rangbestimmung \\
                 11.1. {\"A}quivalente Matrizen / 89 \\
                 11.2. Der Gausssche Algorithmus / 90 \\
                 11.3. Die Normalform / 93 \\
                 11.4. Darstellung durch Matrizenmultiplikation / 94 \\
                 11.5. Ein Beispiel / 96 \\
                 11.6. Rang von Matrizenprodukten / 97 \\
                 III. Kapitel. Formen und Transformationen \\
                 12. Bilineare und quadratische Formen \\
                 12.1. Bilineare Formen / 99 \\
                 12.2. Quadratische Formen / 101 \\
                 12.3. Definite quadratische Formen / 102 \\
                 12.4. Kriterien und S{\"a}tze zur Definitheit / 103 \\
                 12.5. Die Gausssche Transformation / 106 \\
                 12.6. Geometrische Deutungen. Tensorfl{\"a}che / 108
                 \\
                 13. Koordinaten transformationen \\
                 13.1. Transformation quadratischer Formen / 111 \\
                 13.2. Beispiele / 113 \\
                 13.3. Transformation einer Bilinearform / 116 \\
                 13.4. Transformation linearer Vektorfunktionen / 117
                 \\
                 IV. Kapitel. Das Eigenwertproblem \\
                 14. Charakteristische Zahlen und Eigen vektoren \\
                 14.1. Problemstellung und Begriffe / 120 \\
                 14.2. Die Eigenvektoren / 122 \\
                 14.3. Beispiele / 125 \\
                 14.4. {\"A}hnlichkeitstransformation, Invarianten / 129
                 \\
                 14.5. Matrizenpotenzen / 131 \\
                 14.6. Absch{\"a}tzung der charakteristischen Zahlen /
                 133 \\
                 15. Symmetrische Matrizen \\
                 15.1. Charakteristische Zahlen und Eigenvektoren
                 symmetrischer \\
                 Matrizen / 134 \\
                 15.2. Das System der Hauptachsen / 136 \\
                 15.3. Das Orthogonalisierungsverfahren / 138 \\
                 15.4. Beispiele / 139 \\
                 15.5. Maximaleigenschaften der charakteristischen
                 Zahlen / 142 \\
                 15.6. Der Entwicklungssatz / 143 \\
                 15.7. Hauptachsentransformation symmetrischer Matrizen
                 / 145 \\
                 15.8. Hauptachsentransformation quadratischer Formen
                 1.47 \\
                 15.9. Ein Beispiel / 148 \\
                 15.10. Allgemeine Normalform. Das Tr{\"a}gheitsgesetz /
                 149 \\
                 15.11. Tensorfl{\"a}chen und Verzerrungsellipsoid / 151
                 \\
                 16. Allgemeinere Eigenwertprobleme \\
                 16.1. Die allgemeine Eigenwertaufgabe. Matrizenpaare /
                 152 \\
                 16.2. Aufgabe der Zwischenstufe / 157 \\
                 16.3. Hauptkoordinatentransformation von Matrizenpaaren
                 / 159 \\
                 16.4. Orthogonalit{\"a}tseigenschaft bei allgemeinen
                 Matrizen / 160 \\
                 16.5. Hauptachsensystempaar und verallgemeinerte
                 Hauptachsentransformation / 162 \\
                 16.6. Geometrische Deutung der allgemeinen reellen
                 Lineartransformation / 165 \\
                 17. Komplexe Matrizen \\
                 17.1. Komplexe Matrizen und ihre Sonderformen / 167 \\
                 17.2. Hermitesche Formen / 171 \\
                 17.3. Charakteristische Zahlen und Eigenvektoren / 172
                 \\
                 17.4. Die Matrix $\overbar{\mathfrak{A}}' \mathfrak{A}$
                 / 176 \\
                 V. Kapitel. Struktur der Matrix \\
                 18. Die Minimumgleichung \\
                 18.1. Die Cayley--Hamiltonsche Gleichung / 180 \\
                 18.2. Minimumgleichung der Matrix / 183 \\
                 18.3. Begleitmatrix und Jordan-Matrix / 184 \\
                 19. Elementarteiler, Klassifikation \\
                 19.1. Determinantenteiler, invariante Faktoren und
                 Elementarteiler / 186 \\
                 19.2. Minimumgleichung und Rangabfall / 188 \\
                 19.3. Charakteristik und Klassifikation / 190 \\
                 19.4. {\"A}quivalenz von Polynommatrizen / 192 \\
                 19.5. Die Smithsche Normalform / 194 \\
                 19.6. Ein Beispiel / 197 \\
                 20. Die Normalform \\
                 20.1. Die Jordansehe Normalform / 198 \\
                 20.2. Eine weitere Normalform / 202 \\
                 20.3. Gegenseitige Orthogonalit{\"a}t der Eigenvektoren
                 von $\mathfrak{A}$ und $\mathfrak{A}'$ / 203 \\
                 20.4. Matrizenpaare / 205 \\
                 20.5. Kongruente Matrizen / 208 \\
                 21. Hauptvektoren. Transformation auf Normalform \\
                 21.1. Problemstellung / 211 \\
                 21.2. Die Weyrschen Charakteristiken / 212 \\
                 21.3. Die Hauptvektoren / 214 \\
                 21.4. Transformation auf die Normalform / 216 \\
                 21.6. Ein Beispiel / 224 \\
                 21.7. Verallgemeinerte Hauptvektoren bei Matrizenpaaren
                 / 226 \\
                 22. Matrizenfunktionen und Matrizengleichungen \\
                 22.1. Charakteristische Zahlen einer Matrizenfunktion /
                 227 \\
                 22.2. Reduktion der Matrizenfunktion auf das
                 Ersatzpolynom / 228 \\
                 22.3. Andere Form des Ersatzpolynoms. Mehrfachwurzeln /
                 230 \\
                 22.4. Durch Potenzreihen darstellbare
                 Matrizenfunktionen / 233 \\
                 22.5. Beispiele / 236 \\
                 22.6. Die Neul{\i}annsche Reihe / 238 \\
                 22.7. Allgemeinere Definition der Matrizenfunktion /
                 240 \\
                 22.8. Lineare Matrizengleichungen / 242 \\
                 22.9. Die Gleichungen $\mathfrak{X}^m = 0$ und
                 $\mathfrak{X} = \mathfrak{E}$ / 245 \\
                 22.10. Allgemeine algebraische Matrizengleichungen /
                 246 \\
                 VI. Kapitel. Numerische Verfahren, \\
                 23. Aufl{\"o}sung linearer Gleichungssysteme durch
                 Matrizenmultiplikation \\
                 23.1. Das abgek{\"u}rzte Verfahren von Gauss in
                 Matrizenform (Banachiewicz) / 248 \\
                 23.2. Bestimmung der Elemente $b_{i k}$ und $c_{i k}$ /
                 252 \\
                 23.3. Rechenschema und Proben / 253 \\
                 23.4. Die Zahlenrechnung / 256 \\
                 23.5. Ein Zahlenbeispiel / 258 \\
                 23.6. Abweichungen vom Regelfall / 259 \\
                 23.7. Vereinfachung bei symmetrischen Matrizen.
                 Verfahren von \\
                 Cholesky / 260 \\
                 23.8. Berechnung der Kehrmatrix / 263 \\
                 23.9. Komplexe Gleichungssysteme / 269 \\
                 24. Iterative Behandlung linearer Gleichungssysteme \\
                 24.1. {\"U}bersicht / 270 \\
                 24.2. Das Gauss--Seidelsche Iterationsverfahren / 272
                 \\
                 24.3. Relaxationsmethode nach Gauss--Southwell / 276
                 \\
                 24.4. Konvergenzbeschleunigung nach Gauss / 280 \\
                 24.5. Nachtr{\"a}gliche Korrekturen / 282 \\
                 25. Iterative Bestimmung der gr{\"o}{\ss}ten
                 charakteristischen \\
                 Zahl \\
                 25.1. Das Iterationsverfahren bei reeller symmetrischer
                 Matrix / 285 \\
                 25.2. Bestimmung einer weiteren charakteristischen Zahl
                 / 290 \\
                 25.3. Betragsgleiche charakteristische Zahlen
                 symmetrischer Matrizen / 292 \\
                 25.4. Einschlie{\ss}ungsverfahren von Collatz / 293 \\
                 25.5. Komplexe charakteristische Zahl $\lambda_1$ / 296
                 \\
                 25.6. Verhalten bei nichtlinearen Elementarteilern.
                 Konvergenzbeschleunigung / 299 \\
                 25.7. Die allgemeine Eigenwertaufgabe / 304 \\
                 26. Bestimmung h{\"o}herer Eigenwerte \\
                 26.1. Verfahren von Koch / 305 \\
                 26.2. Verfahren der reduzierten Matrix / 306 \\
                 26.3. Gebrochene Iteration nach Wielandt / 311 \\
                 26.4. Verfahren von Frazer--Duncan--Collar / 314 \\
                 26.5. Verfahren von Hessenberg / 316 \\
                 26.6. Vollst{\"a}ndiges Rechenschema nebst Summenproben
                 zum Verfahren von Hessenberg / 322 \\
                 26.7. Eigenwertberechnung bei komplexen Matrizen / 325
                 \\
                 VII. Kapitel. Anwendungen \\
                 27. Matrizen in der Elektrotechnik \\
                 27.1. Berechnung allgemeiner Netzwerke / 330 \\
                 27.2. Erg{\"a}nzende Bemerkungen / 336 \\
                 27.3. Ein Beispiel: Dreiphasentransformator / 337 \\
                 27.4. Drehstromsysteme in symmetrischen Komponenten /
                 339 \\
                 27.5. Matrizen in der Vierpoltheorie / 343 \\
                 27.6. Bemerkungen zum Schrifttum / 347 \\
                 28. Matrizen in der Schwingungstechnik \\
                 28.1. Theorie der unged{\"a}mpften kleinen Schwingungen
                 / 348 \\
                 28.2. Hauptkoordinaten. Kopplung / 352 \\
                 28.3. Kontinuierliche Schwingungssysteme / 354 \\
                 28.4. Schwingungssysteme mit D{\"a}mpfung. Frage der
                 Stabilit{\"a}t / 355 \\
                 28.5. Iterative Behandlung ged{\"a}mpfter
                 Schwingungssysteme / 359 \\
                 28.6. Klassifikation ged{\"a}mpfter
                 Schwingungsvorg{\"a}nge / 361 \\
                 29. Systeme linearer Differentialgleichungen \\
                 29.1. Lineare Differentialgleichungssysteme erster
                 Ordnung mit konstanten Koeffizienten / 366 \\
                 29.2. Verhalten bei nichtlinearen Elementarteilern /
                 368 \\
                 29.3. Ein Beispiel / 372 \\
                 29.4. Differentialgleichungssysteme h{\"o}herer Ordnung
                 / 373 \\
                 29.5. Ein Beispiel / 375 \\
                 30. Differentialmatrizen und nichtlineare
                 Transformationen \\
                 30.1. Differentialmatrizen / 377 \\
                 30.2. Ein Beispiel / 380 \\
                 30.3. Nichtlineare Transformationen / 381 \\
                 30.4. Krummlinige Koordinaten / 384 \\
                 30.5. Orthogonale Koordinaten / 385 \\
                 30.6. Differentialausdr{\"u}cke der Vektorrechnung /
                 387 \\
                 30.7. Ein Beispiel / 390 \\
                 31. Tensoren \\
                 31.1. Begriff des Tensors / 392 \\
                 31.2. Der Tr{\"a}gheitstensor / 393 \\
                 31.3. Spannungs- und Dehnungstensor / 397 \\
                 31.4. Verallgemeinerter Tensorbegriff / 402 \\
                 32. Matrizen in der Ausgleichsrechnung \\
                 32.1. Grundz{\"u}ge der Ausgleichsrechnung / 406 \\
                 32.2. Matrizenschreibweise / 408 \\
                 32.3. Beobachtungen ungleicher Genauigkeit. Gewichte /
                 410 \\
                 32.4. Umkehrung der Gleichungen / 411 \\
                 32.5. Mittlerer Fehler der Ausgleichsgr{\"o}{\ss}en
                 $x$, $y$, / 414 \\
                 32.6. Herleitung des mittleren Fehlers $m$ / 417 \\
                 Sachverzeichnis / 419",
}

@Book{Zurmuhl:1958:MDI,
  author =       "Rudolf Zurm{\"u}hl",
  title =        "{Matrizen: Eine Darstellung f{\"u}r Ingenieure}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xv + 467",
  year =         "1958",
  ISBN =         "3-642-53291-8",
  ISBN-13 =      "978-3-642-53291-7",
  LCCN =         "QA188.Z8 1958; QA263 .Z8 1958",
  bibdate =      "Sun Nov 23 13:39:47 MST 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  URL =          "http://d-nb.info/1028197780/3;
                 http://nbn-resolving.de/urn:nbn:de:1111-201211261057;
                 http://www.springerlink.com/content/978-3-642-53291-7",
  acknowledgement = ack-nhfb,
  author-dates = "1904--1966",
  language =     "German",
  subject =      "Matrices; Matrizenrechnung; Matrizenrechnung;
                 Matrices; Matrices; Matrices; Lineare Algebra; Matrix
                 (Mathematik); Matrizenrechnung.",
  tableofcontents = "I. Kapitel. Der Matrizenkalk{\"u}l \\
                 1. Grundbegriffe und einfache Rechenregeln \\
                 1.1. Lineare Transformation, Matrix und Vektor / 1 \\
                 1.2. Zeilen und Spaltenvektoren / 5 \\
                 1.3. Einfache Rechenregeln / 7 \\
                 1.4. Transponierte Matrix, symmetrische und
                 schiefsymmetrische Matrix / 9 \\
                 1.5. Diagonalmatrix, Skalarmatrix und Einheitsmatrix /
                 11 \\
                 1.6. Lineare Abh{\"a}ngigkeit, Rang, singul{\"a}re
                 Matrix, Determinante / 12 \\
                 2. Das Matrizenprodukt / 15 \\
                 2.1. Einf{\"u}hrung des Matrizenproduktes / 15 \\
                 2.2. S{\"a}tze {\"u}ber Matrizenmultiplikation / 20 \\
                 2.3. Diagonal- und verwandte Matrizen / 23 \\
                 2.4. Skalares Produkt, Norm = Betrag und 'Vinkel von
                 Vektoren / 25 \\
                 2.5. Dyadisches Produkt / 26 \\
                 2.6. Potenzen und Polynome / 28 \\
                 2.7. Die Gausssche Transformation $\mathfrak{U}'
                 \mathfrak{U}$ / 29 \\
                 2.8. Orthogonale Matrizen / 30 \\
                 3. Die Kehrmatrix / 32 \\
                 3.1. Begriff und Herleitung der Kehrmatrix / 32 \\
                 3.2. Adjungierte Matrix. Formelm{\"a}{\ss}iger Ausdruck
                 der $\alpha_{i k}$ / 35 \\
                 3.3. Matrizendivision / 38 \\
                 4. Komplexe Matrizen / 39 \\
                 4.1. Komplexe Matrizen und Vektoren / 39 \\
                 4.2. Sonderformen komplexer Matrizen / 41 \\
                 4.3. Reelle Form komplexer Matrizen / 44 \\
                 5. Lineare Abbildungen und Koordinatentransformationen.
                 / 47 \\
                 5.1. Lineare Abbildungen / 47 \\
                 5.2. Darstellung durch Matrizen / 50 \\
                 5.3. Koordinatentransformation / 52 \\
                 5.4. Hintereinanderschalten linearer Transformationen /
                 54 \\
                 5.5. Beispiele / 55 \\
                 5.6. Orthogonale Transformationen / 59 \\
                 5.7. Kontragrediente Transformation und Kongruenz / 60
                 \\
                 II. Kapitel. Lineare Gleichungen \\
                 6. Der Gausssche Algorithmus / 62 \\
                 6.1. Prinzip des Algorithmus / 62 \\
                 6.2. Verketteter Algorithmus als Matrizenoperation / 64
                 \\
                 6.3. Symmetrische Koeffizientenmatrix. Verfahren von
                 Cholesky / 70 \\
                 6.4. Reihenvertauschung bei $b_{i i} = 0$ / 72 \\
                 6.5. Divisionsfreier Algorithmus / 77 \\
                 6.6. Berechnung der Kehrmatrix. Matrizendivision / 78
                 \\
                 6.7. Kehrmatrix bei symmetrischer Matrix / 81 \\
                 7. Lineare Abh{\"a}ngigkeit und Rang / 83 \\
                 7.1. Lineare Abh{\"a}ngigkeit eines Vektorsystems / 83
                 \\
                 7.2. Der Rang einer Matrix / 86 \\
                 7.3. Rang von Matrizenprodukten / 90 \\
                 7.4. {\"A}quivalenz / 95 \\
                 8. Allgemeine lineare Gleichungssysteme / 97 \\
                 8.1. Allgemeine homogene Gleichungssysteme / 97 \\
                 8.2. Allgemeine inhomogene Gleichungssysteme / 102 \\
                 9. Orthogonalsysteme / 105 \\
                 9.1. Orthogonalisierung eines Vektorsystems / 105 \\
                 9.2. Vollst{\"a}ndiges Orthogonalsystem / 107 \\
                 9.3. Biorthogonalsysteme / 110 \\
                 9.4. Vollst{\"a}ndiges Biorthogonalsystem / 113 \\
                 9.5. Halbinverse einer Rechteckmatrix / 116 \\
                 10. Polynommatrizen und ganzzahlige Matrizen / 119 \\
                 10.1. Parametermatrizen. Charakteristische Determinante
                 und Rangabfall / 119 \\
                 10.2. Polynommatrizen und ganzzahlige Matrizen.
                 {\"A}quivalenz / 121 \\
                 10.3. Die Smithsche Normalform. Elementarpolynome und
                 Elementarteiler / 124 \\
                 III. Kapitel. Quadratische Formen nebst Anwendungen \\
                 11. Quadratische Formen / 129 \\
                 11.1. Darstellung quadratischer und bilinearer Formen /
                 129 \\
                 11.2. Positiv definite quadratische Formen / 131 \\
                 11.3. Transformation quadratischer Formen. Kongruenz /
                 134 \\
                 11.4. Hermitesche Formen / 137 \\
                 11.5. Geometrische Deutung / 139 \\
                 12. Einige Anwendungen des Matrizenkalk{\"u}ls / 141
                 \\
                 12.1. Anwendung in der Ausgleichsrechnung / 141 \\
                 12.2. Berechnung von Fachwerken / 144 \\
                 12.3. Behandlung von Schwingungsaufgaben / 146 \\
                 IV. Kapitel. Das Eigenwertproblem \\
                 13. Eigenwerte und Eigenvektoren / 150 \\
                 13.1. Problemstellung und Begriffe / 150 \\
                 13.2. Die Eigenvektoren / 152 \\
                 13.3. Beispiele / 155 \\
                 13.4. {\"A}hnlichkeitstransformation. Invarianten / 158
                 \\
                 13.5. Matrizenpotenzen. Matrizenprodukte / 160 \\
                 13.6. Die allgemeine Eigenwertaufgabe / 163 \\
                 14. Diagonal{\"a}hnliche Matrizen / 165 \\
                 14.1. Das System der Eigenachsen. Transformation auf
                 Diagonalform / 165 \\
                 14.2. Linkseigenvektoren. Orthogonalit{\"a}t / 166 \\
                 14.3. Der Entwicklungssatz. Verfahren von
                 Krylov--Frazer--Duncan--Collar / 169 \\
                 14.4. Cayley--Hamiltonsche Gleichung und
                 Minimumgleichung / 176 \\
                 14.5. Das v. Misessche Iterationsverfahren / 179 \\
                 14.6. Spektralzerlegung diagonal{\"a}hnlicher Matrizen
                 / 180 \\
                 15. Symmetrische Matrizen / 182 \\
                 15.1. Eigenwerte und Eigenvektoren symmetrischer
                 Matrizen / 182 \\
                 15.2. Extremaleigenschaften der Eigenwerte / 185 \\
                 15.3. Extremaleigenschaft, Fortsetzung / 188 \\
                 15.4. Anwendung auf quadratische Formen / 190 \\
                 15.5. Allgemeine Eigenwertaufgabe / 192 \\
                 16. Normale Matrizen. Die Matrix $\mathfrak{U}'
                 \mathfrak{U}$. Absch{\"a}tzungen / 194 \\
                 16.1. Symmetrisierbare Matrizen / 194 \\
                 16.2. Normale und normalisierbare Matrizen / 196 \\
                 16.3. Hauptachsensystempaar einer allgemeinen Matrix /
                 199 \\
                 16.4. Produktdarstellung als Drehstreckung. Radizieren
                 einer Matrix / 201 \\
                 16.5. Absch{\"a}tzung der Eigenwerte / 203 \\
                 16.6. Wertebereich einer Matrix. Weitere
                 Absch{\"a}tzungen / 206 \\
                 * 17. Eigenwerte spezieller Matrizen / 210 \\
                 17.1. Schief-Hermitesche und unit{\"a}re Matrizen / 210
                 \\
                 17.2. Nichtnegative Matrizen.
                 Einschlie{\ss}ungss{\"a}tze / 212 \\
                 17.3. Spaltensummenkonstante und stochastische Matrizen
                 / 215 \\
                 17.4. Schachbrettmatrizen / 217 \\
                 17.5 Differenzenmatrizen / 222 \\
                 17.6. Matrizen zyklischer Bauart / 224 \\
                 17.7. Frobenius' Begleitmatrix / 225 \\
                 V. Kapitel. Struktur der Matrix \\
                 18. Minimumgleichung, Charakteristik und Klassifikation
                 / 228 \\
                 18.1. Die Minimumgleichung / 228 \\
                 18.2. Determinantenteiler, Elementarpolynome und
                 Elementarteiler / 231 \\
                 18.3. Minimalpolynom. Rangabfall / 233 \\
                 18.4. Charakteristik und Klassifikation einer Matrix /
                 234 \\
                 18.5. Matrizenpaare, simultane {\"A}quivalenz und
                 {\"A}hnlichkeit / 237 \\
                 19. Die Normalform. Hauptvektoren und Hauptvektorketten
                 / 239 \\
                 19.1. Die Jordansche Normalform / 239 \\
                 19.2. Orthogonalit{\"a}t von Rechts- und
                 Linkseigenvektoren / 242 \\
                 19.3. Die Weyrschen Charakteristiken / 245 \\
                 19.4. Die Hauptvektoren / 247 \\
                 19.5. Aufbau der Hauptvektorketten / 251 \\
                 20. Matrizenfunktionen und Matrizengleich ungen / 256
                 \\
                 20.1. Eigenwerte einer Matrizenfunktion / 256 \\
                 20.2. Reduktion der Matrizenfunktion auf das
                 Ersatzpolynom / 258 \\
                 20.3. Matrizenpotenzreihen und durch sie darstellbare
                 Matrizenfunktionen / 261 \\
                 20.4. Beispiele / 263 \\
                 20.5. Allgemeinere Definition der Matrizenfunktion /
                 264 \\
                 20.6. Lineare Matrizengleichungen / 267 \\
                 20.7. Die Gleichungen $\mathfrak{X}^m = 0$ und
                 $\mathfrak{X}^m = \mathfrak{G}$ / 270 \\
                 20.8. Allgemeine algebraische Matrizengleichung / 271
                 \\
                 VI. Kapitel. Numerische Verfahren \\
                 21. Eigenwertaufgabe: Iterative Verfahren / 273 \\
                 21.1. Das v. Misessche Iterationsverfahren: Zur
                 Rechentechnik / 273 \\
                 21.2. Betragsgleiche reelle Eigenwerte / 276 \\
                 21.3. Komplexer Eigenwert / 277 \\
                 21.4. Simultaniteration mehrerer Eigenwerte / 281 \\
                 21.5. Der Rayleigh-Quotient und seine Verallgemeinerung
                 / 282 \\
                 21.6. Gebrochene Iteration / 286 \\
                 21.7. Verbesserung durch gebrochene Iteration / 287 \\
                 21.8. Bestimmung h{\"o}herer Eigenwerte: Verfahren von
                 Koch / 292 \\
                 21.9. H{\"o}here Eigenwerte durch Matrizenreduktion /
                 294 \\
                 21.10. Nichtlineare Elementarteiler / 299 \\
                 22. Eigenwertaufgabe: Direkte Verfahren / 303 \\
                 22.1. Interpolation / 303 \\
                 22.2. Zum Verfahren von Krylov--Frazer--Duncan--Collar.
                 / 304 \\
                 22.3. Verfahren von Hessenberg / 306 \\
                 22.4. Hessenberg: Aufbau des charakteristischen
                 Polynoms / 309 \\
                 22.5. Hessenberg: Bestimmung der Eigenvektoren / 312
                 \\
                 22.6. Hessenberg: Abweichung vom Regelfall / 313 \\
                 22.7. Eigenwertberechnung bei komplexer Matrix / 317
                 \\
                 23. Iterative Behandlung linearer Gleichungssysteme /
                 320 \\
                 23.1. Das Gauss--Seidelsche Iterationsverfahren / 320
                 \\
                 23.2. Iteration mit Elimination / 323 \\
                 23.3. Konvergenz und Fehlerabsch{\"a}tzung / 325 \\
                 23.4. Relaxation nach Gauss--Southwell / 328 \\
                 23.5. Iterative Nachbehandlung / 334 \\
                 23.6. Verfahren der conjugierten Gradienten
                 ($cg$-Verfahren) von Hestenes--Stiefel / 336 \\
                 VII. Kapitel. Anwendungen \\
                 24. Matrizen in der Elektrotechnik / 344 \\
                 24.1. Allgemeine Transformationsgesetze f{\"u}r
                 Str{\"o}me und Spannungen / 344 \\
                 24.2. Allgemeine Netzberechnung: Umlaufverfahren / 346
                 \\
                 24.3. Netzberechnung: Knotenpunktsverfahren / 350 \\
                 24.4. Knotenpunktsbelastete Netze / 354 \\
                 24.5. Unsymmetrisch belastete Drehstromsysteme.
                 Symmetrische Komponenten / 358 \\
                 24.6. Matrizen in der Vierpoltheorie / 362 \\
                 25. Anwendungen in der Statik / 364 \\
                 25.1. Lasten und Spannungen, Verschiebungen und
                 Verformungen / 364 \\
                 25.2. Die elastischen Verformungen / 367 \\
                 25.3. Berechnung der statisch Unbestimmten / 369 \\
                 25.4. Spannungen durch thermische und andere
                 Verformungen / 370 \\
                 25.5. Zwei Beispiele / 371 \\
                 25.6. Berechnung modifizierter Systeme / 377 \\
                 25.7. Verschiebungsmethode / 379 \\
                 26. {\"u}bertragungsmatrizen zur Behandlung
                 elastomechanischer \\
                 Aufgaben / 482 \\
                 26.1. Prinzip / 482 \\
                 26.2. Biegeschwingungen / 385 \\
                 26.3. Diskrete Federn und Massen: Punkt- und
                 Leitmatrizen / 390 \\
                 26.4. Innere Randbedingungen / 393 \\
                 26.5. Determinantenmatrizen / 395 \\
                 26.6. Aufgaben der Balkenbiegung / 403 \\
                 26.7. Biegeschwingung: Direkte Frequenzberechnung / 408
                 \\
                 26.8. Beispiele / 416 \\
                 27. Matrizen in der Schwingungstechnik / 424 \\
                 27.1. Unged{\"a}mpfte Schwingungssysteme endlicher
                 Freiheitsgrade / 424 \\
                 27.2. Iterative Behandlung der Aufgabe / 427 \\
                 27.3. Kontinuierliche Schwingungssysteme / 430 \\
                 27.4. Schwingungssysteme mit D{\"a}mpfung. Frage der
                 Stabilit{\"a}t / 431 \\
                 27.5. Iterative Behandlung ged{\"a}mpfter
                 Schwingungssysteme / 435 \\
                 27.6. Klassifikation ged{\"a}mpfter Schwingungssysteme
                 / 436 \\
                 28. Systeme linearer Differentialgleichungen / 441 \\
                 28.1. Homogene Systeme erster Ordnung mit konstanten
                 Koeffizienten / 441 \\
                 28.2. Verhalten bei nichtlinearen Elementarteilern /
                 446 \\
                 28.3. Systeme h{\"o}herer Ordnung / 450 \\
                 28.4. Inhomogene Systeme / 454 \\
                 28.5. Nichtkonstante Koeffizienten / 457 \\
                 Sachverzeichnis / 462",
}

@Book{Zurmuhl:1961:MIT,
  author =       "Rudolf Zurm{\"u}hl",
  title =        "{Matrizen und ihre technischen Anwendungen}.
                 ({German}) [{Matrices} and their technical
                 applications]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "459",
  year =         "1961",
  LCCN =         "QA263 .Z8 1961",
  bibdate =      "Sun Nov 23 13:36:32 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1904--",
  language =     "German",
  subject =      "Matrices",
}

@Book{Zurmuhl:1964:MIT,
  author =       "Rudolf Zurm{\"u}hl",
  title =        "{Matrizen und ihre technischen Anwendungen}.
                 ({German}) [{Matrices} and their technical
                 applications]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Fourth",
  pages =        "xii + 452",
  year =         "1964",
  LCCN =         "QA263 .Z8 1964",
  bibdate =      "Sun Nov 23 13:36:32 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1904--",
  language =     "German",
  remark =       "Errata slip inserted. First to second editions
                 published under title: Matrizen, eine Darstellung
                 f{\"u}r Ingenieure.",
  subject =      "Matrices",
}

@Book{Zurmuhl:1984:MIA,
  author =       "Rudolf Zurm{\"u}hl and Sigurd Falk",
  title =        "{Matrizen und ihre Anwendungen f{\"u}r angewandte
                 Mathematiker, Physiker und Ingenieure. Teil 1.
                 Grundlagen}. ({German}) [{Matrices} and their Uses for
                 Applied Mathematicians, Physicists, and Engineers.
                 {Part 1}. {Foundations}]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Fifth",
  pages =        "xiv + 342",
  year =         "1984",
  ISBN =         "0-387-03238-X, 0-387-12848-4 (New York), 3-540-12848-4
                 (Berlin)",
  ISBN-13 =      "978-0-387-03238-2, 978-0-387-12848-1 (New York),
                 978-3-540-12848-9 (Berlin)",
  LCCN =         "QA188 .Z87 1984",
  MRclass =      "15-01 (00A69)",
  MRnumber =     "758259 (86a:15002)",
  MRreviewer =   "S. Lajos",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Grundlagen. [Foundations]",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  language =     "German",
  tableofcontents = "I. Kapitel. Der Matrizenkalk{\"u}l \\
                 1. Grundbegriffe und einfache Rechenregeln / 1 \\
                 1.1. Lineare Transformation, Matrix und Vektor / 1 \\
                 1.2. Zeilen- und Spaltenvektoren / 5 \\
                 1.3. Einfache Rechenregeln / 7 \\
                 1.4. Transponierte Matrix, symmetrische und
                 schiefsymmetrische Matrix / 9 \\
                 1.5. Diagonalmatrix, Skalarrnatrix und Einheitsmatrix /
                 11 \\
                 1.6. Lineare Abh{\"a}ngigkeit, Rang, singul{\"a}re
                 Matrix, Determinante / 12 \\
                 2. Das Matrizenprodukt / 15 \\
                 2.1. Einf{\"u}hrung des Matrizenproduktes / 15 \\
                 2.2. S{\"a}tze {\"u}ber Matrizenmultiplikation / 20 \\
                 2.3. Diagonal- und verwandte Matrizen / 23 \\
                 2.4. Skalares Produkt, Betrag und Winkel reeller
                 Vektoren / 25 \\
                 2.5. Dyadisches Produkt / 27 \\
                 2.6. Potenzen und Polynome / 29 \\
                 2.7. Die Gau{\ss}sche Transformation / 30 \\
                 2.8. Orthogonale Matrizen / 31 \\
                 3. Die Kehrmatrix / 33 \\
                 3.1. Begriff und Herleitung der Kehrmatrix / 33 \\
                 3.2. Adjungierte Matrix. Formelm{\"a}{\ss}iger Ausdruck
                 der $\alpha_{i k}$ / 36 \\
                 3.3. Matrizendivision / 39 \\
                 4. Komplexe Matrizen / 40 \\
                 4.1. Komplexe Matrizen und Vektoren / 40 \\
                 4.2. Sonderformen komplexer Matrizen / 42 \\
                 4.3. Reelle Form komplexer Matrizen / 45 \\
                 5. Lineare Abbildungen und Koordinatentransformationen
                 / 48 \\
                 5.1. Lineare Abbildungen / 48 \\
                 5.2. Darstellung durch Matrizen / 51 \\
                 5.3. Koordinatentransformation / 53 \\
                 5.4. Orthogonale Transformationen / 55 \\
                 5.5. Kontragrediente Transformation und Kongruenz / 56
                 \\
                 5.6. Abschlie{\ss}ende Bemerkung. Ausblick / 57 \\
                 II. Kapitel. Lineare Gleichungen \\
                 6. Der Gau{\ss}sche Algorithmus / 58 \\
                 6.1. Prinzip des Algorithmus / 58 \\
                 6.2. Verketteter Algorithmus als Matrizenoperation / 60
                 \\
                 6.3. Symmetrische Koeffizientenmatrix. Verfahren von
                 Cholesky / 66 \\
                 6.4. Reihenvertauschung bei $b_{i i} = 0$ / 68 \\
                 6.5. Der Gau{\ss}sche Algorithmus als Transformation /
                 73 \\
                 6.6. Berechnung der Kehrmatrix. Matrizendivision / 75
                 \\
                 6.7. Kehrmatrix bei symmetrischer Matrix / 77 \\
                 7. Lineare Abh{\"a}ngigkeit und Rang / 79 \\
                 7.1. Lineare Abh{\"a}ngigkeit eines Vektorsystems / 79
                 \\
                 7.2. Der Rang einer Matrix / 82 \\
                 7.3. Rang von Matrizenprodukten / 86 \\
                 7.4. {\"A}quivalenz / 91 \\
                 8. Allgemeine lineare Gleichungssysteme / 93 \\
                 8.1. Allgemeine homogene Gleichungssysteme / 93 \\
                 8.2. Allgemeine inhomogene Gleichungssysteme / 98 \\
                 9. Orthogonalsysteme / 101 \\
                 9.1. Orthogonalisierung eines Vektorsystems / 101 \\
                 9.2. Vollst{\"a}ndiges Orthogonalsystem / 103 \\
                 9.3. Biorthogonalsysteme / 106 \\
                 9.4. Vollst{\"a}ndiges Biorthogonalsystem / 109 \\
                 9.5. Halbinverse einer Rechteckmatrix / 112 \\
                 10. Polynommatrizen und ganzzahlige Matrizen / 115 \\
                 10.1. Parametermatrizen. Charakteristische Determinante
                 und Rangabfall / 115 \\
                 10.2. Polynommatrizen und ganzzahlige Matrizen. {\"A}
                 quivalenz / 117 \\
                 10.3. Die Smithsche Normalform. Elementarpolynome und
                 Elementarteiler / 120 \\
                 III. Kapitel. Quadratische Formen nebst Anwendungen \\
                 11 Quadratische Formen / 125 \\
                 11.1. Darstellung quadratischer und bilinearer Formen /
                 125 \\
                 11.2. Positiv definite quadratische Formen / 127 \\
                 11.3. Transformation quadratischer Formen. Kongruenz /
                 130 \\
                 11.4. Hermitesche Formen / 133 \\
                 11.5. Geometrische Deutung / 135 \\
                 12. Einige Anwendungen quadratischer Formen / 137 \\
                 12.1. Anwendung in der Ausgleichsrechnung / 137 \\
                 12.2. Vektorielles Produkt und Abstandsquadrat / 140
                 \\
                 12.3. Massen- und Fl{\"a}chenmoment zweiten Grades /
                 141 \\
                 12.4. Die kinetische Energie eines starren K{\"o}rpers
                 / 144 \\
                 12.5. Die potentielle Energie einer elastischen Feder /
                 145 \\
                 IV. Kapitel. Die Eigenwertaufgabe \\
                 13. Eigenwerte und Eigenvektoren / 146 \\
                 13.1. Problemstellung und Begriffe / 146 \\
                 13.2. Die Eigenvektoren / 148 \\
                 13.3. Beispiele / 151 \\
                 13.4. Linkseigenvektoren. Orthogonalit{\"a}t / 155 \\
                 13.5. {\"A}hnlichkeitstransformation. Invarianten / 157
                 \\
                 13.6. Der Rayleigh-Quotient. Wertebereich einer Matrix
                 / 158 \\
                 13.7. Matrizenpotenzen. Matrizenprodukte / 161 \\
                 13.8. Die allgemeine Eigenwertauf g{\"a}be / 164 \\
                 13.9. Eigenwertberechnung bei komplexer Matrix / 166
                 \\
                 14. Diagonal{\"a}hnliche Matrizen / 168 \\
                 14.1. Das System der Eigenachsen. Transformation auf
                 Diagonalform / 168 \\
                 14.2. Der Entwicklungssatz. Verfahren von Krylov / 170
                 \\
                 14.3. Cayley--Hamiltonsche Gleichung und
                 Minimumgleichung / 177 \\
                 14.4. Diagonal{\"a}hnliche Matrizenpaare / 180 \\
                 14.5. Spektralzerlegung eines diagonal{\"a}hnlichen
                 Matrizenpaares. Eigenterme und Eigenwerte / 182 \\
                 15. Symmetrische und hermitesche Matrizen / 186 \\
                 15.1. Eigenwerte und Eigenvektoren / 186 \\
                 15.2.Extremaleigenschaften der Eigenwerte / 188 \\
                 15.3. Extremaleigenschaft, Fortsetzung / 189 \\
                 15.4. Anwendung auf quadratische Formen / 191 \\
                 15.5. Allgemeine Eigenwertaufgabe / 193 \\
                 15.6. Schiefhermitesche und unit{\"a}re Matrizen / 195
                 \\
                 16. Normale und normalisierbare Matrizen / 196 \\
                 16.1. Symmetrisierbare Matrizen / 197 \\
                 16.2. Normale und normalisierbare Matrizen / 198 \\
                 16.3. Normale Matrizenpaare. Spektralzerlegung / 202
                 \\
                 16.4. Der Rayleigh-Quotient. Wertebereich eines
                 normalen Matrizenpaares / 207 \\
                 16.5. Hauptachsensystempaar einer allgemeinen Matrix /
                 210 \\
                 16.6. Produktdarstellung als Drehstreckung. Radizieren
                 einer Matrix / 212 \\
                 16.7. Singul{\"a}re Werte eines Matrizenpaares / 213
                 \\
                 16.8. Fragen der Normierung / 217 \\
                 16.9. Schlu{\ss}bemerkung. Ausblick / 219 \\
                 17. Eigenwerte spezieller Matrizen / 220 \\
                 17.1. Nichtnegative Matrizen.
                 Einschlie{\ss}ungss{\"a}tze / 220 \\
                 17.2. Spaltensummenkonstante und stochastische Matrizen
                 / 222 \\
                 17.3. Schachbrettmatrizen / 225 \\
                 17.4. Zyklische Matrizen / 229 \\
                 17.5. Die Differenzenmatrix zweiter Ordnung / 230 \\
                 V. Kapitel. Struktur der Matrix \\
                 18. Minimumgleichung, Charakteristik und Klassifikation
                 / 234 \\
                 18.1. Die Minimumgleichung / 234 \\
                 18.2. Determinantente{\"u}er, Elementarpolynome und
                 Elementarteuer / 237 \\
                 18.3. Minimalpolynom. Rangabfall / 239 \\
                 18.4. Charakteristik und Klassifikation einer Matrix /
                 240 \\
                 18.5. Matrizenpaare, simultane {\"A}quivalenz und
                 {\"A}hnlichkeit / 243 \\
                 19. Die Normalform. Hauptvektoren und Hauptvektorketten
                 / 245 \\
                 19.1. Die Jordansche Normalform / 245 \\
                 19.2. Orthogonalit{\"a}t von Rechts- und
                 Linkseigenvektoren / 248 \\
                 19.3. Die Weyrschen Charakteristiken / 251 \\
                 19.4. Die Hauptvektoren / 253 \\
                 19.5. Aufbau der Hauptvektorketten / 257 \\
                 20. Matrizenfunktionen und Matrizengleichungen / 262
                 \\
                 20.1. Eigenwerte einer Matrizenfunktion / 262 \\
                 20.2. Reduktion der Matrizenfunktion auf das
                 Ersatzpolynom / 264 \\
                 20.3. Matrizenpotenzreihen und durch sie darstellbare
                 Matrizenfunktionen / 267 \\
                 20.4. Beispiele / 269 \\
                 20.5. Allgemeinere Definition der Matrizenfunktion /
                 270 \\
                 20.6. Lineare Matrizengleichungen / 273 \\
                 20.7. Die Gleichungen $X^m = 0$ und $X^m = I$ / 276 \\
                 20.8. Allgemeine algebraische Matrizengleichung / 277
                 \\
                 21. Parametermatrizen / 279 \\
                 21.1. Problemstellung / 279 \\
                 21.2. Spektralzerlegung einer diagonal{\"a}hnlichen
                 Parametermatrix / 279 \\
                 21.3. Diagonal{\"a}hnliche Matrizentupel / 284 \\
                 21.4. Selbstnormierende Tupel / 286 \\
                 21.5. {\"U}ber die Eigenwerte von Matrizenprodukten /
                 287 \\
                 21.6. Parameternormale Matrizen / 289 \\
                 21.7. Lineare Abh{\"a}ngigkeit von einem Leitpaar / 293
                 \\
                 VI. Kapitel. Blockmatrizen \\
                 22. Definitionen, S{\"a}tze und Regeln / 295 \\
                 22.1. Die Matrizenmultiplikation in Bl{\"o}cken / 295
                 \\
                 22.2. Die reduzierte Blockmatrix / 297 \\
                 22.3. Blockdreiecksmatrizen / 302 \\
                 22.4. Inverse und Adjungierte einer vierteiligen
                 Hypermatrix / 303 \\
                 22.5. Die Identit{\"a}t von Frobenius/Schur/Woodbury /
                 308 \\
                 22.6. Abge{\"a}nderte (gest{\"o}rte, benachbarte)
                 Gleichungssysteme / 311 \\
                 22.7. Abge{\"a}nderte Bilinearformen / 314 \\
                 22.8. Singul{\"a}re Matrizenpaare / 315 \\
                 23. Expansion von Polynomen und Polynommatrizen / 320
                 \\
                 23.1. Zielsetzung / 320 \\
                 23.2. Expansion von Polynomen / 320 \\
                 23.3. G{\"u}nther-Expansion einer Polynommatrix / 322
                 \\
                 23.4. Elliptische Diagonalexpansion einer Polynommatrix
                 / 323 \\
                 23.5. Parabolische und hyperbolische Diagonalexpansion
                 / 328 \\
                 23.6. Wiederholte Diagonalexpansion / 331 \\
                 23.7. Zusammenfassung / 333 \\
                 Schlu{\ss}bemerkung / 333 \\
                 Weiterf{\"u}hrende Literatur / 334 \\
                 Namen- und Sachverzeichnis / 335",
}

@Book{Zurmuhl:1986:MIA,
  author =       "Rudolf Zurm{\"u}hl and Sigurd Falk",
  title =        "{Matrizen und ihre Anwendungen f{\"u}r angewandte
                 Mathematiker, Physiker und Ingenieure. Teil 2.
                 Numerische Methoden}. ({German}) [{Matrices} and their
                 Uses for Applied Mathematicians, Physicists, and
                 Engineers. {Part 2}. {Numerical} Methods]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Fifth",
  pages =        "xvi + 476",
  year =         "1986",
  DOI =          "https://doi.org/10.1007/978-3-642-61614-3",
  ISBN =         "0-387-15474-4 (New York hardcover), 3-540-15474-4
                 (Berlin hardcover)",
  ISBN-13 =      "978-0-387-15474-9 (New York hardcover),
                 978-3-540-15474-7 (Berlin hardcover)",
  LCCN =         "QA188 .Z87 1984",
  MRclass =      "65Fxx (15-02 15A90 65-02)",
  MRnumber =     "877099 (88g:65024)",
  MRreviewer =   "A. Bunse-Gerstner",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Numerische Methoden. [Numerical methods]",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  language =     "German",
  tableofcontents = "VII. Kapitel. Grundz{\"u}ge der Matrizennumerik \\
                 24. Grundbegriffe und einfache Rechenregeln / 1 \\
                 24.1. Reine Mathematik, Numerische Mathematik und
                 Angewandte Mathematik. Einige Vorbemerkungen / 1 \\
                 24.2. Die L{\"a}nge einer Operationskette.
                 Vorw{\"a}rts- und R{\"u}ckw{\"a}rtsrechnen / 6 \\
                 24.3. Verfahren mit Vorgabeverlust / 8 \\
                 24.4. Matrizen mit ausgepr{\"a}gtem Profil / 9 \\
                 24.5. Die f{\"u}nf Lesearten eines Matrizenproduktes /
                 42 \\
                 24.6. Die Matrizenmultiplikation von Winograd / 13 \\
                 24.7. Die geometrische Reihe / 15 \\
                 24.8. Blockspektralmatrix und Blockmodalmatrix / 18 \\
                 24.9. Der Sylvester-Test f{\"u}r hermitesche Paare / 19
                 \\
                 24.10. Die additive Zerlegung einer hermiteschen Matrix
                 / 20 \\
                 24.11. Taylor-Entwicklung einer Parametermatrix.
                 Ableitung der charakteristischen Gleichung / 21 \\
                 24.12. Konstruktion von Matrizen mit vorgegebenen
                 Eigenschaften. Testmatrizen / 24 \\
                 24.13. Skalierung einer Zahlenfolge. Die
                 $\epsilon$-Jordan-Matrix / 28 \\
                 24.14. Fokussierung / 29 \\
                 24.15. Rechenaufwand f{\"u}r die gebr{\"a}uchlichsten
                 Matrizenoperationen / 31 \\
                 25. Norm, Kondition, Korrektur und Defekt / 33 \\
                 25.1. Die Norm eines Vektors / 33 \\
                 25.2. Die Norm einer Matrix / 34 \\
                 25.3. Norm und Eigenwertabsch{\"a}tzung / 39 \\
                 25.4. Das normierte Defektquadrat (Norm III) / 40 \\
                 25.5. Die Kondition einer Matrix. Skalierung.
                 Sensibilit{\"a}t / 45 \\
                 25.6. Defekt und Korrektur / 50 \\
                 26. Kondensation und Ritzsches Verfahren / 51 \\
                 26.1. Die Matrizenhauptgleichung und der
                 Alternativsatz. Resonanz und Scheinresonanz / 51 \\
                 26.2. Kondensation als Teil f{\"u}r das Ganze / 55 \\
                 26.3. Hermitesche Paare. Der Trennungssatz / 58 \\
                 26.4. Hermitesche Kondensation / 61 \\
                 26.5. Lokaler Zerfall einer Parametermatrix.
                 Bereinigung. Die Zentr{\"a}lgleichung / 61 \\
                 26.6. Zentraltransformation und Minimumvektor. Splitten
                 eines Vektors / 67 \\
                 26.7. Die Optimaltransformation / 71 \\
                 26.8. Kondensation einer quadratischen Form / 72 \\
                 VIII. Kapitel. Theorie und Praxis der Transformationen
                 \\
                 27. Eine allgemeine Transformationstheorie / 77 \\
                 27.1. {\"U}berblick. Zielsetzung / 77 \\
                 27.2. {\"A}quivalenz und {\"A}hnlichkeit (Kongruenz) /
                 80 \\
                 27.3. Das Generalschema einer multiplikativen
                 Transformation / 81 \\
                 27.4. Der Transport durch die Informationsklammer.
                 Phantommatrix / 83 \\
                 27.5. Diskrepanz und Regeneration / 85 \\
                 27.6. Die Zur{\"u}cknahme einer
                 {\"A}quivalenztransformation / 86 \\
                 27.7. Unit{\"a}re (orthonormierte) Transformation / 87
                 \\
                 27.8. Dyadische Transformationsmatrizen / 88 \\
                 27.9. Unvollst{\"a}ndige und vollst{\"a}ndige Reduktion
                 eines Vektors. Der $\epsilon$-Kalfaktor / 94 \\
                 27.10. Der Mechanismus der multiplikativen
                 Transformation / 98 \\
                 27.11. Progressive Transformationen / 101 \\
                 28. {\"A}quivalenztransformation auf Diagonalmatrix /
                 103 \\
                 28.1. Aufgabenstellung / 103 \\
                 28.2. Direkte und indirekte linksseitige
                 {\"A}quivalenztransformation auf Diagonalmatrix / 104
                 \\
                 28.3. Die linksseitige {\"A}quivalenztransformation auf
                 obere Dreiecksmatrix / 105 \\
                 28.4. Singul{\"a}re Matrix. Rangbestimmung / 109 \\
                 28.5. Die Rechtstransformation auf Diagonalmatrix.
                 Normalform / 110 \\
                 28.6. Hermitesche und positiv definite Matrix / 111 \\
                 28.7. Die dyadische Zerlegung von Banachiewicz und
                 Cholesky / 113 \\
                 28.8. Die Normalform eines diagonal{\"a}hnlichen
                 Matrizentupels / 115 \\
                 29. {\"A}hnlichkeitstransformation auf
                 Fastdreiecksmatrix / 116 \\
                 29.1. Aufgabenstellung / 116 \\
                 29.2. Der Mechanismus einer multiplikativen
                 {\"A}hnlichkeitstransformation / 117 \\
                 29.3. Multiplikative Transformation auf Hessenbergform
                 / 119 \\
                 29.4. Multiplikative Transformation auf Tridiagonalform
                 / 119 \\
                 29.5. Multiplikative Transformation auf Kodiagonalform
                 / 119 \\
                 29.6. Multiplikative Transformation eines hermiteschen
                 Paares auf Tridiagonalform / 119 \\
                 29.7. Progressive Transformation auf Kodiagonalform
                 (Begleitmatrix) / 120 \\
                 29.8. Progressive Transformation eines hermiteschen
                 Paares auf Tridiagonalform / 121 \\
                 29.9. Der Zerfall einer Fastdreiecksmatrix / 123 \\
                 30. Iterative {\"A}hnlichkeitstransformation auf
                 Dreiecks- bzw. Diagonalform / 126 \\
                 30.1. {\"U}berblick. Zielsetzung / 126 \\
                 30.2. Transformation in Unterr{\"a}umen. Die
                 Elementartransformation / 128 \\
                 30.3. Das explizite Jacobi-Verfahren / 130 \\
                 30.4. Das halbimplizite Jacobi-Verfahren f{\"u}r
                 beliebige Paare G,D / 133 \\
                 30.5. Das halbimplizite Jacobi-Verfahren f{\"u}r
                 beliebige Paare A;B / 138 \\
                 30.6. Die Regeneration (Auffrischung) des
                 Jacobi-Verfahrens. Abge{\"a}nderte (benachbarte,
                 gest{\"o}rte) Paare / 139 \\
                 30.7. Jacobi-{\"a}hnliche Transformationen.
                 Zusammenfassung / 141 \\
                 IX. Kapitel. Lineare Gleichungen und Kehrmatrix \\
                 31. Einschlie{\ss}ung und Fehlerabsch{\"a}tzung.
                 Kondition / 143 \\
                 31.1. Defekt und Korrektur / 143 \\
                 31.2. Einschlie{\ss}ung mittels hermitescher
                 Kondensation (Spektralnorm) / 144 \\
                 31.3. Einschlie{\ss}ung bei diagonaldominanter Matrix /
                 148 \\
                 31.4. Stabilisierung schlecht bestimmter
                 Gleichungssysteme / 149 \\
                 32. Endliche Algorithmen zur Aufl{\"o}sung linearer
                 Gleichungssysteme / 151 \\
                 32.1. Zielsetzung. ,,Endlichkeit'' der Methode / 151
                 \\
                 32.2. Ein- und zweiseitige Transformation / 152 \\
                 32.3. Der Gau{\ss}sche Algorithmus in Bl{\"o}cken / 152
                 \\
                 32.4. Partitionierung einer Block-Hessenberg-Matrix /
                 155 \\
                 32.5. Partitionierung einer Blocktridiagonalmatrix /
                 158 \\
                 32.6. Vierteilung einer Bandmatrix / 163 \\
                 32.7. Die {\"A}quivalenztransformation als dyadische
                 Zerlegung. Exogene und endogene Algorithmen / 165 \\
                 32.8. Die Kongruenztransformation als dyadische
                 Zerlegung. Das Verfahren von Hestenes und Stiefel / 167
                 \\
                 32.9. Mehrschrittverfahren / 174 \\
                 32.10. Zusammenfassung / 175 \\
                 33. Iterative und halbiterative Methoden zur
                 Aufl{\"o}sung von linearen Gleichungssystemen / 176 \\
                 33.1. Allgemeines. {\"U}berblick / 176 \\
                 33.2. Station{\"a}re Treppeniteration
                 (Gau{\ss}--Seidel-{\"a}hnliche Verfahren) / 177 \\
                 33.3. Instation{\"a}re Treppeniteration. Der
                 Algorithmus ,,Siebenmeilenstiefel'' / 180 \\
                 33.4. Korrektur und Diskrepanz. Nachiteration / 182 \\
                 33.5. Abge{\"a}nderte (benachbarte, gest{\"o}rte)
                 Gleichungssysteme / 183 \\
                 33.6. Der restringierte Ritz-Ansatz / 186 \\
                 33.7. Das normierte Defektquadrat / 187 \\
                 33.8. Der zyklisch fortgesetzte Ritz-Ansatz.
                 Minimalrelaxation / 189 \\
                 33.9. {\"U}ber- und Unterrelaxation / 192 \\
                 33.10. Der vollst{\"a}ndige Ritz-Ansatz / 192 \\
                 33.11. Eine generelle Kritik / 193 \\
                 33.12. Der Algorithmus Rapido/Rapidissimo / 194 \\
                 33.13. Nochmals Nachiteration. Abge{\"a}nderte
                 (benachbarte, gest{\"o}rte) Gleichungssysteme / 197 \\
                 33.14. Zusammenfassung / 200 \\
                 34. Kehrmatrix. Endliche und iterative Methoden / 203
                 \\
                 34.1. {\"U}bersicht. Zielsetzung / 203 \\
                 34.2. Aufl{\"o}sung des Gleichungssystems $A K = I$ /
                 203 \\
                 34.3. Die Eskalatormethode der sukzessiven
                 R{\"a}nderung / 205 \\
                 34.4. Das Verfahren von Schulz / 207 \\
                 34.5. Einschlie{\ss}ung der Elemente einer Kehrmatrix /
                 209 \\
                 X. Kapitel. Die lineare Eigenwertaufgabe \\
                 35. Spektralumordnung und Partitionierung / 211 \\
                 35.1. {\"U}berblick. Zielsetzung / 211 \\
                 35.2. Umordnung des Spektrums mit Hilfe von
                 Matrizenfunktionen. Schiftstrategien / 211 \\
                 35.3. Umordnung des Spektrums mit Hilfe von
                 Eigendyaden. Deflation / 214 \\
                 35.4. Partitionierung durch unvollst{\"a}ndige
                 Hauptachsentransformation. Ordnungserniedrigung / 216
                 \\
                 35.5. Elementarmatrizen und Austauschverfahren / 219
                 \\
                 35.6. Sukzessive Ausl{\"o}schung. Produktzerlegung der
                 Modalmatrizen / 223 \\
                 35.7. Bereinigung und lokaler Zerfall einer Matrix /
                 226 \\
                 35.8. Besonderheiten bei singul{\"a}rer Matrix B / 226
                 \\
                 35.9. Transformation auf obere Dreiecksmatrix / 228 \\
                 35.10. Einf{\"u}hrung von Linkseigenvektoren / 230 \\
                 36. Einschlie{\ss}ungss{\"a}tze f{\"u}r Eigenwerte und
                 Eigenvektoren / 233 \\
                 36.1. {\"U}berblick. Wozu Einschlie{\ss}ungss{\"a}tze ?
                 / 233 \\
                 36.2. Die S{\"a}tze von Gerschgorin und Heinrich. Der
                 Kreisringsatz / 235 \\
                 36.3. Einschlie{\ss}ung isolierbarer Eigenwerte bei
                 Diagonaldominanz / 239 \\
                 36.4. Quotientens{\"a}tze. Der Rayleigh-Quotient / 239
                 \\
                 36.5. Der Satz von Krylov und Bogoljubov und seine
                 Versch{\"a}rfung von Temple / 242 \\
                 36.6. Der Perturbationssatz f{\"u}r hermitesche Paare /
                 245 \\
                 36.7. Der Satz Acta Mechanica f{\"u}r hermitesche
                 positiv definite Paare / 248 \\
                 36.8. Der Satz Acta Mechanica f{\"u}r normale Paare /
                 255 \\
                 36.9. Der Satz Acta Mechanica mit vorgezogener
                 Zentraltransformation / 259 \\
                 36.10. Der Determinantensatz / 260 \\
                 36.11. Komponentenweise Einschlie{\ss}ung von Eigen
                 Vektoren normaler Paare / 267 \\
                 36.12. Einschlie{\ss}ung bei Mammutmatrizen / 269 \\
                 36.13. Zusammenfassung. Schlu{\ss}bemerkung / 270 \\
                 37. Determinantenalgorithmen / 271 \\
                 37.1. {\"U}bersicht / 271 \\
                 37.2. Die direkte Methode. Explizites und implizites
                 Vorgehen / 272 \\
                 37.3. Systematisierte Suchmethoden / 274 \\
                 37.4. Die Ritz-Iteration / 275 \\
                 37.5. Ritz-Iteration mit vorgezogener
                 Zentraltransformation / 279 \\
                 37.6. Der Algorithmus Bonaventura / 282 \\
                 37.7. Der Algorithmus Securitas. Gleichm{\"a}{\ss}ige
                 Konvergenz gegen das Spektrum / 285 \\
                 37.8. Der Algorithmus Securitas f{\"u}r singul{\"a}re
                 Paare / 293 \\
                 37.9. Einige Varianten zum Algorithmus Securitas / 295
                 \\
                 37.10. Iterative Einschlie{\ss}ung von Eigenwerten /
                 298 \\
                 37.11. Ein Nachtrag / 303 \\
                 38. Extremalalgorithmen / 304 \\
                 38.1. Das Prinzip. {\"U}berblick / 304 \\
                 38.2. Koordinatenrelaxation bei hermiteschen Paaren /
                 305 \\
                 38.3. Defektminimierung durch Schaukeliteration / 305
                 \\
                 38.4. Weitere Extremalalgorithmen. Schlu{\ss}bemerkung
                 / 309 \\
                 39. Unterraumtransformationen / 310 \\
                 39.1. Das Prinzip / 310 \\
                 39.2. Kongruenztransformationen mit Jacobi-Strategie /
                 311 \\
                 39.3. {\"A}hnlichkeitstransformationen mit
                 Jacobi-Strategie / 311 \\
                 39.4. Schlu{\ss}bemerkung / 312 \\
                 40. Potenzalgorithmen / 312 \\
                 40.1. Die Potenziteration nach von Mises / 312 \\
                 40.2. Die Potenziteration f{\"u}r Matrizenpaare / 316
                 \\
                 40.3. Simultaniteration / 319 \\
                 40.4. Iteration gegen Linkseigenvektoren. Verbesserter
                 Ritz-Ansatz und Spektralumordnung / 325 \\
                 40.5. Die inverse (gebrochene) Iteration von Wielandt /
                 326 \\
                 40.6. Ma{\ss}nahmen zur Konvergenzbeschleunigung / 328
                 \\
                 40.7. Ritz-Ansatz oder Orthonormierung? Ein
                 Kompromi{\ss} / 329 \\
                 40.8. Simultaniteration mit n Startvektoren. Direkte
                 Unitarisierung / 330 \\
                 40.9. Dreiecks- und Diagonalalgorithmen / 331 \\
                 40.10. {\"A}quivalenztransformation auf obere
                 Dreiecksmatrix / 334 \\
                 40.11. {\"A}hnlichkeitstransformation auf obere
                 Dreiecksmatrix / 338 \\
                 40.12. Kongruenztransformation hermitescher Paare auf
                 Diagonalmatrix / 342 \\
                 40.13. Transformation auf obere Blockdreiecksmatrix /
                 343 \\
                 40.14. Dreiecks- und Diagonalalgorithmen mit
                 progressivem Schift / 345 \\
                 40.15. Sukzessive Ordnungserniedrigung oder
                 gleichm{\"a}{\ss}ige Konvergenz gegen das Spektrum ? /
                 349 \\
                 40.16. Gleichm{\"a}{\ss}ige Konvergenz gegen das
                 Spektrum durch partielle {\"A}hnlichkeitstransformation
                 / 351 \\
                 40.17. Die Transformation singul{\"a}rer Matrizen auf
                 Normalform / 356 \\
                 40.18. Der WSS-Algorithmus (Wielandt-Iteration mit
                 sequentiellem Schift) / 359 \\
                 40.19. Der WSS-Algorithmus f{\"u}r normale Paare / 363
                 \\
                 40.20. Der Globalalgorithmus Velocitas / 364 \\
                 40.21. Singul{\"a}re Paare / 370 \\
                 Res{\"u}mee zum X. Kapitel. Was will der Praktiker? /
                 371 \\
                 XI. Kapitel. Die nichtlineare Eigenwertaufgabe \\
                 41. Die nichtlineare Eigenwertaufgabe mit einem
                 Parameter / 378 \\
                 41.1. {\"U}berblick. Zielsetzung / 378 \\
                 41.2. Polynommatrizen. Expansion / 379 \\
                 41.3. Parameterdiagonal{\"a}hnliche und
                 parameternormale Polynommatrizen / 382 \\
                 41.4. Die Bequemlichkeitshypothese. (Modale
                 D{\"a}mpfung) / 383 \\
                 41.5. Der Algorithmus Bonaventura / 390 \\
                 41.6. Die Taylor-Entwicklung des Schur-Komplements.
                 (Der T--S-Algorithmus) / 392 \\
                 41.7. Der T--S-Algorithmus mit h{\"o}heren Ableitungen
                 / 398 \\
                 41.8. Defektminimierung / 400 \\
                 41.9. Parameterabh{\"a}ngige Transformationsmatrizen /
                 401 \\
                 41.10. Einschlie{\ss}ungss{\"a}tze / 402 \\
                 41.11. Zusammenfassung und Ausblick / 402 \\
                 42. Das mehrparametrige Eigenwertproblem / 403 \\
                 42.1. Aufgabenstellung. Probleme und Begriffe / 403 \\
                 42.2. Parameterdiagonal{\"a}hnliche und
                 parameternormale Matrizen / 404 \\
                 42.3. Das zweiparametrige Eigenwertproblem / 406 \\
                 XII. Kapitel. Matrizen in der Angewandten Mathematik
                 und Mechanik \\
                 43. Aufl{\"o}sung skalarer Gleichungen durch Expansion.
                 Der Eigenwertalgorithmus ECP / 410 \\
                 43.1. Problemstellung / 410 \\
                 43.2. L{\"o}sung algebraischer Gleichungen durch
                 Diagonalexpansion / 411 \\
                 43.3. Einschlie{\ss}ung von Nullstellen / 414 \\
                 43.4. Die inverse Iteration von Wielandt / 415 \\
                 43.5. Ritz-Iteration und Bonaventura / 417 \\
                 43.6. Iterative Einschlie{\ss}ung und sukzessive
                 Aktualisierung. Globalalgorithmus / 422 \\
                 43.7. Der Eigenwertalgorithmus ECP (Expansion des
                 charakteristischen Polynoms) / 425 \\
                 43.8. Zur Wahl der St{\"u}tzwerte / 431 \\
                 43.9. Zusammenfassung / 434 \\
                 Res{\"u}mee zu den numerischen Methoden / 435 \\
                 44. Die linearisierte Mechanik von
                 Starrk{\"o}rperverb{\"a}nden / 438 \\
                 44.1. Die linearisierte Mechanik / 438 \\
                 44.2. Der frei bewegliche Verband von starren
                 K{\"o}rpern / 440 \\
                 44.3. Offene und geschlossene Schreibweise. Elimination
                 und Kondensation / 441 \\
                 44.4. Bindungen und Reaktionen / 443 \\
                 44.5. Die ebene Gelenkkette / 445 \\
                 45. Diskretisierung und Finitisierung hybrider
                 Strukturen / 451 \\
                 45.1. Problemstellung / 451 \\
                 45.2. Diskrete Modelle / 452 \\
                 45.3. Der {\"U}bergang zum Kontinuum / 452 \\
                 45.4. Finite {\"U}bersetzungen / 457 \\
                 45.5. Hybride Systeme / 457 \\
                 45.6. Finite-Elemente-Methoden (FEM) / 458 \\
                 45.7. Zusammenschau / 460 \\
                 Literatur zu Teil 1 und Teil 2 / 461 \\
                 Namen- und Sachverzeichnis / 471",
}

@Book{Todd:1962:SNA,
  editor =       "John Todd",
  booktitle =    "Survey of Numerical Analysis",
  title =        "Survey of Numerical Analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xvi + 589",
  year =         "1962",
  LCCN =         "QA297 .T6",
  MRclass =      "65.00",
  MRnumber =     "0135221 (24 \#B1271)",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  URL =          "http://en.wikipedia.org/wiki/John_Todd_(computer_scientist)",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  author-dates = "May 16, 1911--June 21, 2007",
}

@Book{Young:1972:SNM,
  author =       "David M. Young and Robert Todd Gregory",
  title =        "A Survey of Numerical Mathematics",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "x + 492 (A1--A18 and B1--B14 and I1--I19)",
  year =         "1972",
  ISBN =         "0-201-08773-1, 0-486-65691-8 (Dover paperback)",
  ISBN-13 =      "978-0-201-08773-4, 978-0-486-65691-5 (Dover
                 paperback)",
  LCCN =         "QA297 .Y63 1972",
  MRclass =      "65-02",
  MRnumber =     "53 11954a",
  bibdate =      "Wed Jan 17 10:57:04 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "D. Greenspan",
  tableofcontents = "1: Numerical Analysis as a Subject Area \\
                 1.1 Introduction \\
                 1.2 Some pitfalls in computation \\
                 1.3 Mathematical and computer aspects of an algorithm
                 \\
                 1.4 Numerical instability of algorithms and
                 ill-conditioned problems \\
                 1.5 Typical problems of interest to the numerical
                 analyst \\
                 1.6 Iterative methods \\
                 2: Elementary Operations with Automatic Digital
                 Computers \\
                 2.1 Introduction \\
                 2.2 Binary arithmetic \\
                 2.3 Conversion from base $D$ to base $B$ representation
                 \\
                 2.4 Representation of integers on a binary computer \\
                 2.5 Floating-point representations \\
                 2.6 Computer-representable numbers \\
                 2.7 Floating-point arithmetic operations \\
                 2.8 Fortran analysis of a floating-point number \\
                 2.9 Calculation of elementary functions \\
                 3: Surveillance of Number Ranges \\
                 3.1 Introduction \\
                 3.2 Allowable number ranges \\
                 3.3 Basic real arithmetic operations \\
                 3.4 The quadratic equation \\
                 3.5 Complex arithmetic operations \\
                 4: Solution of Equations \\
                 4.1 Introduction \\
                 4.2 Attainable accuracy \\
                 4.3 Graphical methods \\
                 4.4 The method of bisection \\
                 4.5 The method of false position \\
                 4.6 The secant method \\
                 4.7 General properties of iterative methods \\
                 4.8 Generation of iterative methods \\
                 4.9 The Newton method \\
                 4.10 Muller's method \\
                 4.11 Orders of convergence of iterative methods \\
                 4.12 Acceleration of the convergence \\
                 4.13 Systems of nonlinear equations \\
                 5: Roots of Polynomial Equations \\
                 5.1 Introduction \\
                 5.2 General properties of polynomials \\
                 5.3 The Newton method and related methods \\
                 5.4 Muller's method and Cauchy's method \\
                 5.5 Location of the roots \\
                 5.6 Root acceptance and refinement \\
                 5.7 Matrix related methods: the modified Bernoulli
                 method \\
                 5.8 Matrix related methods: the IP method \\
                 5.9 Polyalgorithms \\
                 5.10 Other methods \\
                 6: Interpolation and Approximation \\
                 6.1 Introduction \\
                 6.2 Linear interpolation \\
                 6.3 Convergence and accuracy of linear interpolation
                 \\
                 6.4 Lagrangian interpolation \\
                 6.5 Convergence and accuracy of Lagrangian
                 interpolation \\
                 6.6 Interpolation with equal intervals \\
                 6.7 Hermite interpolation \\
                 6.8 Limitations on polynomial interpolation: smooth
                 interpolation \\
                 6.9 Inverse interpolation \\
                 6.10 Approximation by polynomials \\
                 6.11 Least squares approximation by polynomials \\
                 6.12 Rational approximation \\
                 6.13 Trigonometric interpolation and approximation \\
                 6.14 Interpolation in two variables \\
                 7: Numerical Differentiation and Quadrature \\
                 7.1 Introduction \\
                 7.2 The method of undetermined weights \\
                 7.3 Numerical differentiation \\
                 7.4 Numerical quadrature --- equal intervals \\
                 7.5 The Euler--MacLaurin formula \\
                 7.6 Romberg integration \\
                 7.7 Error determination \\
                 7.8 Numerical quadrature --- unequal intervals \\
                 8: Ordinary Differential Equations \\
                 8.1 Introduction \\
                 8.2 Existence and uniqueness \\
                 8.3 Analytic methods \\
                 8.4 Integral equation formulation --- the Picard method
                 of successive approximations \\
                 8.5 The Euler method \\
                 8.6 Methods based on numerical quadrature \\
                 8.7 Error estimation for predictor-corrector methods
                 \\
                 8.8 A numerical example \\
                 8.9 Runge--Kutta methods \\
                 8.10 Methods based on numerical differentiation \\
                 8.11 Higher-order equations and systems of first-order
                 equations \\
                 8.12 The use of high-speed computers \\
                 Appendix A \\
                 Appendix B \\
                 Appendix C \\
                 Bibliography \\
                 Index",
}

@Book{Young:1973:SNM,
  author =       "David M. Young and Robert Todd Gregory",
  title =        "A Survey of Numerical Mathematics",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "493--1099 + xviii + xvi + xviii",
  year =         "1973",
  LCCN =         "QA297 .Y63",
  MRclass =      "65-02",
  MRnumber =     "53 11954b",
  bibdate =      "Wed Jan 17 10:56:05 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "D. Greenspan",
  xxISBN =       "none",
}

@Book{Young:1988:SNMa,
  author =       "David M. Young and Robert Todd Gregory",
  title =        "A Survey of Numerical Mathematics",
  volume =       "I",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "x + 492 + A22 + B16 + I18",
  year =         "1988",
  ISBN =         "0-486-65691-8",
  ISBN-13 =      "978-0-486-65691-5",
  LCCN =         "QA297.Y63 1972",
  MRclass =      "65-02",
  MRnumber =     "92b:65005b",
  bibdate =      "Wed Jan 17 10:30:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Corrected reprint of the 1973 original.",
  URL =          "http://www.zentralblatt-math.org/zmath/en/search/?an=0732.65002",
  ZMnumber =     "0732.65002",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Numerical Analysis as a Subject Area \\
                 1.1 Introduction \\
                 1.2 Some pitfalls in computation \\
                 1.3 Mathematical and computer aspects of an algorithm
                 \\
                 1.4 Numerical instability of algorithms and
                 ill-conditioned problems \\
                 1.5 Typical problems of interest to the numerical
                 analyst \\
                 1.6 Iterative methods \\
                 2: Elementary Operations with Automatic Digital
                 Computers \\
                 2.1 Introduction \\
                 2.2 Binary arithmetic \\
                 2.3 Conversion from base $D$ to base $B$ representation
                 \\
                 2.4 Representation of integers on a binary computer \\
                 2.5 Floating-point representations \\
                 2.6 Computer-representable numbers \\
                 2.7 Floating-point arithmetic operations \\
                 2.8 Fortran analysis of a floating-point number \\
                 2.9 Calculation of elementary functions \\
                 3: Surveillance of Number Ranges \\
                 3.1 Introduction \\
                 3.2 Allowable number ranges \\
                 3.3 Basic real arithmetic operations \\
                 3.4 The quadratic equation \\
                 3.5 Complex arithmetic operations \\
                 4: Solution of Equations \\
                 4.1 Introduction \\
                 4.2 Attainable accuracy \\
                 4.3 Graphical methods \\
                 4.4 The method of bisection \\
                 4.5 The method of false position \\
                 4.6 The secant method \\
                 4.7 General properties of iterative methods \\
                 4.8 Generation of iterative methods \\
                 4.9 The Newton method \\
                 4.10 Muller's method \\
                 4.11 Orders of convergence of iterative methods \\
                 4.12 Acceleration of the convergence \\
                 4.13 Systems of nonlinear equations \\
                 5: Roots of Polynomial Equations \\
                 5.1 Introduction \\
                 5.2 General properties of polynomials \\
                 5.3 The Newton method and related methods \\
                 5.4 Muller's method and Cauchy's method \\
                 5.5 Location of the roots \\
                 5.6 Root acceptance and refinement \\
                 5.7 Matrix related methods: the modified Bernoulli
                 method \\
                 5.8 Matrix related methods: the IP method \\
                 5.9 Polyalgorithms \\
                 5.10 Other methods \\
                 6: Interpolation and Approximation \\
                 6.1 Introduction \\
                 6.2 Linear interpolation \\
                 6.3 Convergence and accuracy of linear interpolation
                 \\
                 6.4 Lagrangian interpolation \\
                 6.5 Convergence and accuracy of Lagrangian
                 interpolation \\
                 6.6 Interpolation with equal intervals \\
                 6.7 Hermite interpolation \\
                 6.8 Limitations on polynomial interpolation: smooth
                 interpolation \\
                 6.9 Inverse interpolation \\
                 6.10 Approximation by polynomials \\
                 6.11 Least squares approximation by polynomials \\
                 6.12 Rational approximation \\
                 6.13 Trigonometric interpolation and approximation \\
                 6.14 Interpolation in two variables \\
                 7: Numerical Differentiation and Quadrature \\
                 7.1 Introduction \\
                 7.2 The method of undetermined weights \\
                 7.3 Numerical differentiation \\
                 7.4 Numerical quadrature --- equal intervals \\
                 7.5 The Euler--MacLaurin formula \\
                 7.6 Romberg integration \\
                 7.7 Error determination \\
                 7.8 Numerical quadrature --- unequal intervals \\
                 8: Ordinary Differential Equations \\
                 8.1 Introduction \\
                 8.2 Existence and uniqueness \\
                 8.3 Analytic methods \\
                 8.4 Integral equation formulation --- the Picard method
                 of successive approximations \\
                 8.5 The Euler method \\
                 8.6 Methods based on numerical quadrature \\
                 8.7 Error estimation for predictor-corrector methods
                 \\
                 8.8 A numerical example \\
                 8.9 Runge--Kutta methods \\
                 8.10 Methods based on numerical differentiation \\
                 8.11 Higher-order equations and systems of first-order
                 equations \\
                 8.12 The use of high-speed computers \\
                 Appendix A \\
                 Appendix B \\
                 Appendix C \\
                 Bibliography \\
                 Index",
}

@Book{Young:1988:SNMb,
  author =       "David M. Young and Robert Todd Gregory",
  title =        "A Survey of Numerical Mathematics",
  volume =       "II",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xii + 607 + A18 + B16 + I18",
  year =         "1988",
  ISBN =         "0-486-65692-6",
  ISBN-13 =      "978-0-486-65692-2",
  LCCN =         "QA297.Y63 1972",
  MRclass =      "65-02",
  MRnumber =     "92b:65005b",
  bibdate =      "Wed Jan 17 10:30:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  note =         "Corrected reprint of the 1973 original.",
  URL =          "http://www.zentralblatt-math.org/zmath/en/search/?an=0732.65003",
  ZMnumber =     "0732.65003",
  acknowledgement = ack-nhfb,
}

@Book{Zhang:2005:SCA,
  editor =       "Fuzhen Zhang",
  booktitle =    "The {Schur} Complement and its Applications",
  title =        "The {Schur} Complement and its Applications",
  volume =       "4",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 295",
  year =         "2005",
  DOI =          "https://doi.org/10.1007/b105056",
  ISBN =         "0-387-24271-6 (hardcover), 0-387-24273-2 (e-book)",
  ISBN-13 =      "978-0-387-24271-2 (hardcover), 978-0-387-24273-6
                 (e-book)",
  LCCN =         "QA184.2 .S38 2005",
  MRclass =      "15-06 (62-06 62H20 65-03 65-06)",
  MRnumber =     "2160825 (2006e:15001)",
  MRreviewer =   "Daniel Kressner",
  bibdate =      "Fri Nov 21 06:49:56 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib",
  series =       "Numerical Methods and Algorithms",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0663/2005042750-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0821/2005042750-t.html",
  abstract =     "The Schur complement plays an important role in matrix
                 analysis, statistics, numerical analysis, and many
                 other areas of mathematics and its applications. This
                 book describes the Schur complement as a rich and basic
                 tool in mathematical research and applications and
                 discusses many significant results that illustrate its
                 power and fertility. The eight chapters of the book
                 cover themes and variations on the Schur complement,
                 including its historical development, basic properties,
                 eigenvalue and singular value inequalities, matrix
                 inequalities in both finite and infinite dimensional
                 settings, closure properties, and applications in
                 statistics, probability, and numerical
                 analysis.\par

                 Although the book is primarily intended to serve as a
                 research reference, it will also be useful for graduate
                 and advanced undergraduate courses in mathematics,
                 applied mathematics, and statistics. The contributing
                 authors' exposition makes most of the material
                 accessible to readers with a sound foundation in linear
                 algebra.",
  acknowledgement = ack-nhfb # " and " # ack-rah # " and " # ack-crj,
  tableofcontents = "Preface \\
                 Historical Introduction: Issai Schur and the Early
                 Development of the Schur Complement \\
                 Basic Properties of the Schur Complement \\
                 Eigenvalue and Singular Value Inequalities of Schur
                 Complements \\
                 Block Matrix Techniques \\
                 Closure Properties \\
                 Schur Complements and Matrix Inequalities:
                 Operator-Theoretic Approach \\
                 Schur Complements in Statistics and Probability \\
                 Schur Complements and Applications in Numerical
                 Analysis \\
                 Bibliography \\
                 Notation \\
                 Index",
}

%%% ====================================================================
%%%                          Part 2 (of 2)
%%% Reviews of ``Matrix Analysis'' (first and second editions).
%%%
%%% Bibliography entries, sorted by citation label, with "bibsort":

@Article{Ando:1987:RBA,
  author =       "T. Ando",
  title =        "Review of {{\booktitle{Matrix Analysis}}, by Roger A.
                 Horn and Charles R. Johnson}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "90",
  number =       "??",
  pages =        "245--247",
  month =        may,
  year =         "1987",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/0024-3795(87)90318-1",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Wed Nov 30 13:50:26 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0024379587903181",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
}

@Article{Bart:2015:RBA,
  author =       "Harm Bart",
  title =        "Review of {{\booktitle{Matrix Analysis}}, second
                 edition, Roger A. Horn, Charles R. Johnson. Cambridge
                 University Press, Cambridge, Melbourne etc. (2013),
                 ISBN: 978-0-521-54823-6}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "466",
  number =       "??",
  pages =        "527--529",
  day =          "1",
  month =        feb,
  year =         "2015",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Thu Nov 20 09:04:41 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379514006922",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
}