Factorizations Of Nonnegative Matrices

In this paper, we discuss one important problem in matrix theory— —factorizations of nonnegative matrices. Firstly, we give a necessary and sufficient condition for a (reducible) nonnegative square matrix to be decomposed into a product of a finite number of irreducible nonnegative matrices in chapter 1. We prove it by using Frobenius normal form in combinational matrix theory and associated directed graph in graph theory. In addition, we can limit the number of factors to (at most) three, and construct every factor. Secondly, we discuss the problem of decomposing a nonnegative matrix into a product of fully indecomposable nonnegative matrices in chapter 2.