A Combinatorial Approach to Matrix Theory and It's Applications

Brualdi, Richard A.; Cvetkovic, Agos

ISBN 10: 142008223X / ISBN 13: 9781420082234

Editore: Chapman & Hall/CRC, USA, 2009

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PUBLISHER: Chapman & Hall/CRC DATE/EDITION: 2009, (isbn indicates 2008) BINDING: Hardbound in printed and illustrated glossy paper covered boards, 267 pages. DUST JACKET: No jacket. BOOK CONDITION: I was originally going to list as near fine as it appears to have never been read but, as you can see in the scan, my dog chewed the top front corner. Other than this the book is still near fine, very clean and text unmarked and binding tight. Codice articolo 009242

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Titolo: A Combinatorial Approach to Matrix Theory ...

Casa editrice: Chapman & Hall/CRC, USA

Data di pubblicazione: 2009

Legatura: Hardcover

Condizione: Good

Condizione sovraccoperta: No Jacket

Descrizione articolo

Riassunto:

Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices.

After reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry.

Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.

Informazioni sull?autore:

Richard A. Brualdi, Dragos Cvetkovic