Combinatorial matrix theory [WorldCat Entities]

"This is the first book length exposition of basic results of combinatorial matrix theory, that is, the use of combinatorics and graph theory in matrix theory (and vice versa) and the study of intrinsic properties of matrices viewed as arrays of numbers rather than as algebraic objects. The early chapters deal with the many connections with matrices, graphs, diagraphs and bipartite graphs. The basic theory of network flow is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters treat the permanent of a matrix and latin squares. The final chapter deals with algebraic characterization of combinatorial properties and the use of combinatorial arguments in proving such classical theorems as the Cayley-Hamilton theorem and the Jordan canonical form."
"This is the first book devoted to the exposition of combinatorial matrix theory. It can be used as a graduate course text, but is complete enough for a standard reference work on the basic theory."@en

Combinatorial matrix theory