Combinatorial Matrix Theory

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Richard A. Brualdi (University of Wisconsin, Madison) Herbert J. Ryser (California Institute of Technology)

Combinatorial Matrix Theory

Richard A. Brualdi (University of Wisconsin, Madison), Herbert J. Ryser (California Institute of Technology)

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English

Cambridge University Press
23 January 2014

Algebra; Combinatorics & graph theory

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.

By: Richard A. Brualdi (University of Wisconsin Madison), Herbert J. Ryser (California Institute of Technology)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 39
Dimensions: Height: 229mm, Width: 152mm, Spine: 20mm
Weight: 510g
ISBN: 9781107662605
ISBN 10: 1107662605
Pages: 378
Publication Date: 23 January 2014
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Combinatorial Matrix Theory

"""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"