可分解成不可约矩阵乘积的非负矩阵(英文)

Nonnegative matrices decomposable into products of irreducible nonnegative matrices

给出了一个n阶非负矩阵可以分解成不可约非负矩阵的乘积的充要条件.并且证明了若一个非负矩阵可分解成不可约非负矩阵的乘积,则可以做到因了个数至多是三个.所用的证明方法是构造性的,可以具体写出各个因子.

This paper gave a necessary and sufficient condition for an n × n nonnegative matrix to be decomposed into a product of irreducible nonnegative matrices. It also showed that when such a decomposition is possible, the number of factors can be required to be at most three. The methods used here are constructive, and the factors can be presented.