Limit search to available items
Book Cover
E-book
Author Brualdi, Richard A

Title Combinatorial matrix theory / Richard A. Brualdi, Herbert J. Ryser
Published Cambridge [England] ; New York : Cambridge University Press, 1991

Copies

Description 1 online resource (ix, 367 pages) : illustrations
Series Encyclopedia of mathematics and its applications ; 39
Encyclopedia of mathematics and its applications ; 39.
Contents 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
Summary 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
Bibliography Includes bibliographical references (pages 345-362) and index
Notes Print version record
Subject Matrices.
Combinatorial analysis.
MATHEMATICS -- Matrices.
Combinatorial analysis
Matrices
Kombinatorische Designtheorie
Matrizentheorie
Combinatória.
Matrizes.
Matrices.
Analyse combinatoire.
Form Electronic book
Author Ryser, Herbert John
ISBN 9781107087750
1107087759
9781107325708
1107325706