A Combinatorial Approach to Matrix Theory and Its Applications (Discrete Mathematics and Its Applications, 52, Band 52) - Hardcover

Brualdi, Richard A.; Cvetkovic, Dragos

Hardcover

ISBN 10: 142008223X ISBN 13: 9781420082234

Verlag: Chapman and Hall/CRC, 2008

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

Richard A. Brualdi, Dragos Cvetkovic

Von der hinteren Coverseite

Through combinatorial and graph theoretic tools, this self-contained reference helps readers understand the fundamentals of matrix theory and its applications to science. It develops the theory using graphs to explain the basic matrix construction, formulas, computations, ideas, and results. The authors stress the combinatorial aspects of the topics with other aspects of the theory. Containing material rarely found at this level, the book covers Gersgorin's theorem and extensions, Kronecker product of matrices, sign nonsingular matrices, and evaluation of the permanent. It also includes various exercises.

Details zur Ausgabe

• Verlag: Chapman and Hall/CRC
• Erscheinungsdatum: 2008
• Sprache: Englisch
• ISBN 10: 142008223X
• ISBN 13: 9781420082234
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 267
• Kontakt zum Hersteller: preigu GmbH & Co. KG; mail@preigu.de; ; Lengericher Landstr. 19; Osnabrück; Niedersachsen; 49078; Deutschland