华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (5): 35-44.

• 应用数学,统计学 • 上一篇    下一篇

可分解成不可约矩阵乘积的非负矩阵(英文)

武宏琳   

  1. 华东师范大学数学系,上海200062
  • 收稿日期:2008-03-18 修回日期:2008-04-15 出版日期:2008-09-25 发布日期:2008-09-25
  • 通讯作者: 武宏琳

Nonnegative matrices decomposable into products of irreducible nonnegative matrices(English)

WU Hong-lin   

  1. Department of Mathematics,East China Normal University,Shanghai 200062,China
  • Received:2008-03-18 Revised:2008-04-15 Online:2008-09-25 Published:2008-09-25
  • Contact: WU Hong-lin

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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.

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, 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.

Key words: irreducible matrix, digraph, nonnegative monomial matrix, Frobenius normal form , nonnegative matrix, irreducible matrix, digraph, nonnegative monomial matrix, Frobenius normal form

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