Combinatorial Approach to Matrix Theory and Its Applications

Placing combinatorial and graph-theoretical tools at the forefront of the development of matrix theory this book uses graphs to explain basic matrix construction formulas computations ideas and results. It presents material rarely found in other books at this level including Gersgorin's theorem and its extensions the Kronecker product of matrices sign-nonsingular matrices and the evaluation of the permanent matrix. The authors provide a combinatorial argument for the classical Cayley-Hamilton theorem and a combinatorial proof of the Jordan canonical form of a matrix. They also describe several applications of matrices in electrical engineering physics and chemistry.