Combinatorial Approach to Matrix Theory and Its Applications
CRC Press
A Combinatorial Approach to Matrix Theory and Its ApplicationsAuthor(s): Richard A. Brualdi, agos Cvetkovic\nFormat: Hardback\nPublisher: Taylor & Francis Ltd, United Kingdom\nImprint: Chapman & Hall/CRC\nISBN-13: 9781420082234, 978-1420082234\nSynopsis\nUnlike 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.\n\nAfter reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the Knig 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 t.
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