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  3. Combinatorial Matrix Theory
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2013
      July 1991
      ISBN:
      9781107325708
      9780521322652
      9781107662605
      DOI:
      https://doi.org/10.1017/CBO9781107325708
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.76kg, 380 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.51kg, 378 Pages
      • Subjects:
      Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
      Series:
      Encyclopedia of Mathematics and its Applications (39)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (39)
    Information

    Book description

    This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves. There are chapters dealing with the many connections between matrices, graphs, digraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix, and Latin squares. The final chapter deals with algebraic characterizations of combinatorial properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jordan Canonical Form. The book is sufficiently self-contained for use as a graduate course text, but complete enough for a standard reference work on the basic theory. Thus it will be an essential purchase for combinatorialists, matrix theorists, and those numerical analysts working in numerical linear algebra.

    Reviews

    "A reader who is familiar with basic results in matrix theory will surely be captivated by this concise self-contained introduction to graph theory and combinatorial ideas and reasoning." S. K. Tharthare, Mathematical Reviews

    "...a major addition to the literature of combinatorics." W. T. Tutte, Bulletin of the American Mathematical Society

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