A Combinatorial Approach to Matrix Theory and Its Applications

A Combinatorial Approach to Matrix Theory and Its Applications
ISBN-10
1420082248
ISBN-13
9781420082241
Category
Mathematics
Pages
288
Language
English
Published
2008-08-06
Publisher
CRC Press
Authors
Richard A. Brualdi, Dragos Cvetkovic

Description

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.

Get the book

Amazon.com
Amazon.com
Search the book
eBay.com
eBay.com
Search the book

Similar books