| 可分解成不可约矩阵乘积的非负矩阵(英文) |
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| 引用本文： | 武宏琳. 可分解成不可约矩阵乘积的非负矩阵(英文)[J]. 华东师范大学学报(自然科学版), 2008, 2008(5): 35-44 |
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| 作者姓名： | 武宏琳 |
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| 作者单位： | 华东师范大学,数学系,上海,200062 |
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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 非负矩阵 不可约矩阵 有向图 非负单项矩阵 Frobenius标准型 |
| 收稿时间： | 2008-03-18 |
| 修稿时间： | 2008-04-15 |
Nonnegative matrices decomposable into products of irreducible nonnegative matrices(English) |
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| WU Hong-lin. Nonnegative matrices decomposable into products of irreducible nonnegative matrices(English)[J]. Journal of East China Normal University(Natural Science), 2008, 2008(5): 35-44 |
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| Authors: | WU Hong-lin |
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| Affiliation: | Department of Mathematics,East China Normal University,Shanghai 200062,China |
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| 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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| Keywords: | nonnegative matrix irreducible matrix digraph nonnegative monomial matrix Frobenius normal form |
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