Combinatorial Matrix Theory (Encyclopedia of Mathematics and by Richard A. Brualdi,Herbert J. Ryser

By Richard A. Brualdi,Herbert J. Ryser

This ebook, first released in 1991, is dedicated to the exposition of combinatorial matrix idea. This topic matters itself with using matrix concept and linear algebra in proving ends up in combinatorics (and vice versa), and with the intrinsic homes of matrices considered as arrays of numbers instead of algebraic items in themselves. There are chapters facing the numerous connections among matrices, graphs, digraphs and bipartite graphs. the elemental thought of community flows is constructed which will receive life theorems for matrices with prescribed combinatorial houses and to procure a number of matrix decomposition theorems. different chapters hide the everlasting of a matrix, and Latin squares. the ultimate bankruptcy bargains with algebraic characterizations of combinatorial homes and using combinatorial arguments in proving classical algebraic theorems, together with the Cayley-Hamilton Theorem and the Jordan Canonical shape. The ebook is satisfactorily self-contained to be used as a graduate direction textual content, yet whole sufficient for the standard reference paintings at the simple thought. therefore will probably be an important buy for combinatorialists, matrix theorists, and people numerical analysts operating in numerical linear algebra.

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