A Combinatorial Approach  to Matrix Theory and Its Applications - Richard A. Brualdi, agos Cvetkovic

A Combinatorial Approach to Matrix Theory and Its Applications

Buch | Hardcover
283 Seiten
2008
Chapman & Hall/CRC (Verlag)
978-1-4200-8223-4 (ISBN)
168,35 inkl. MwSt
Placing combinatorial and graph-theoretical tools at the forefront of the development of matrix theory, this book uses graphs to explain basic matrix construction, formulas, computations, ideas, and results.
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.

Richard A. Brualdi, Dragos Cvetkovic

Introduction. Basic Matrix Operations. Powers of Matrices. Determinants. Matrix Inverses. Systems of Linear Equations. Spectrum of a Matrix. Nonnegative Matrices. Additional Topics. Applications.

Erscheint lt. Verlag 1.11.2008
Reihe/Serie Discrete Mathematics and Its Applications
Zusatzinfo 44 Illustrations, black and white
Sprache englisch
Maße 156 x 234 mm
Gewicht 240 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 1-4200-8223-X / 142008223X
ISBN-13 978-1-4200-8223-4 / 9781420082234
Zustand Neuware
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