
Combinatorial Matrix Theory
Cambridge University Press
Published on 26. July 1991
Book
Hardback
380 pages
978-0-521-32265-2 (ISBN)
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 / Votes
"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 SocietyMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 27 mm
Weight
766 gr
ISBN-13
978-0-521-32265-2 (9780521322652)
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Schweitzer Classification
Other editions
Additional editions

Richard A. Brualdi | Herbert J. Ryser
Combinatorial Matrix Theory
Book
01/2014
Cambridge University Press
€76.20
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Richard A. Brualdi | Herbert J. Ryser
Combinatorial Matrix Theory
E-Book
07/2013
1st Edition
Cambridge University Press
€52.99
Available for download
Persons
Author
University of Wisconsin, Madison
California Institute of Technology
Content
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.