Combinatorial matrix theory / Richard A. Brualdi, Herbert J. Ryser.

Format:

Book

Author/Creator:

Brualdi, Richard A., author.

Ryser, Herbert John, author.

Series:

Encyclopedia of mathematics and its applications ; v. 39.

Encyclopedia of mathematics and its applications ; volume 39

Language:

English

Subjects (All):

Matrices.

Combinatorial analysis.

Physical Description:

1 online resource (ix, 367 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1991.

Language Note:

English

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.

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. [345]-362) and index.

ISBN:

1-139-88620-7

1-107-10251-0

1-107-66260-5

1-107-09400-3

1-107-32570-6

1-107-09997-8

1-107-08775-9

1-107-09085-7

OCLC:

853359890