A Combinatorial Approach to Matrix Theory and It's Applications

Un libro in lingua di Brualdi Richard A. Dragos Cvetkovic edito da Taylor & Francis, 2008

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With their unique approach, which includes combinatorial and graph-theoretical to develop basic theorems of matrix theory, Brualdi (mathematics, U. of Wisconsin-Madison) and Cvetkovic (mathematics, U. of Belgrade) make matrix theory relatively simple. They review the basics, such as terminology, graph theory, counting formulas, fields and vector spaces. They then explain the algebra of matrices and introduce the König digraph, matrix powers and their description, and the Coates digraph of a matrix. They use the Coates digraph to define fundamental properties of determinants that include the Binet-Cauchy formula and the Laplace development of the determinant along a row or column, developing the elementary theory of solutions and systems of linear equations, and showing how the Coates digraph can be used to solve a linear system. They proceed to a combinatorial argument for the classical Cayley-Hamilton theorem and describe non-negative matrices and their special properties. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

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