Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graphtheoretical 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 Konig digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graphtheoretical definition of the determinant using the Coates digraph of a matrix, and presents a graphtheoretical 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 PerronFrobenius theory and study eigenvalue inclusion regions and signnonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. Using combinatorial and graphtheoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.
About Richard A. Brualdi
University of Wisconsin, Madison, USA Mathematical Institute SANU, Belgrade, SerbiaDetails Book
Author  :  Richard A. Brualdi 
Publisher  :  Chapman 
Data Published  :  01 August 2008 
ISBN  :  142008223X 
EAN  :  9781420082234 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  288 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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