Combinatorial matrix theory /

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Bibliographic Details
Author / Creator:Brualdi, Richard A.
Imprint:Cambridge [England] ; New York : Cambridge University Press, 1991.
Description:1 online resource (ix, 367 pages) : illustrations
Language:English
Series:Encyclopedia of mathematics and its applications ; 39
Encyclopedia of mathematics and its applications ; 39.
Subject:Matrices.
Combinatorial analysis.
Matrices.
Analyse combinatoire.
MATHEMATICS -- Matrices.
Combinatorial analysis.
Matrices.
Kombinatorische Designtheorie
Matrizentheorie
CombinatoĢria.
Matrizes.
Matrices.
Analyse combinatoire.
Electronic books.
Konbinatorische Analysis.
Electronic books.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11200354
Hidden Bibliographic Details
Other authors / contributors:Ryser, Herbert John.
ISBN:9781107087750
1107087759
9781107325708
1107325706
0521322650
9780521322652
Notes:Includes bibliographical references (pages 345-362) and index.
Print version record.
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.
Other form:Print version: Brualdi, Richard A. Combinatorial matrix theory. Cambridge [England] ; New York : Cambridge University Press, 1991 0521322650