Nonnegative matrices decomposable into products of irreducible nonnegative matrices(English)
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摘要: 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,则可以做到因子个数至多是三个.所用的证明方法是构造性的,可以具体写出各个因子.
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关键词:
- 非负矩阵 /
- 不可约矩阵 /
- 有向图 /
- 非负单项矩阵 /
- Frobenius标准型
Abstract: This paper gave a necessary and sufficient condition for an n times 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. -
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