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Combinatorial Matrix Theory : Encyclopedia of Mathematics and Its Applications - Richard A. Brualdi

Combinatorial Matrix Theory

Encyclopedia of Mathematics and Its Applications


Published: 29th September 2003
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This is the first book 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.

"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

Incidence matrices
Matrices and graphs
Matrices and digraphs
Matrices and bigraphs
Combinatorial matrix algebra
Existence theorems for combinatorially constrained matrices
Some special graphs
The permanent
Latin squares
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521322652
ISBN-10: 0521322650
Series: Encyclopedia of Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 380
Published: 29th September 2003
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.4 x 15.6  x 2.9
Weight (kg): 0.71