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Combinatorial Matrix Theory (Paperback)
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Combinatorial Matrix Theory (Paperback)
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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.
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