两个矩阵乘积的｛1,2,3｝-逆和｛1,2,4｝-逆的反序律

J4 ›› 2011, Vol. 46 ›› Issue (4): 78-81.

两个矩阵乘积的｛1,2,3｝-逆和｛1,2,4｝-逆的反序律

张凤霞¹,李莹^1,2,赵建立¹

1.聊城大学数学科学学院, 山东聊城 252059; 2.上海理工大学管理学院, 上海 200093

收稿日期:2010-03-12 发布日期:2011-04-21
作者简介:张凤霞(1977- ),女,讲师,硕士,研究方向为矩阵论.Email: zhangfengxia@lcu.edu.cn
基金资助:
国家自然科学基金资助项目(10771073);山东省教育厅科研发展计划资助项目(J09LA05);聊城大学科研基金资助项目(Z09006)

The reverse order law for ｛1,2,3｝-inverse and ｛1,2,4｝-inverse of products of two matrices

ZHANG Feng-xia¹, LI Ying^1,2, ZHAO Jian-li¹

1. School of Mathematics Science, Liaocheng University, Liaocheng 252059, Shandong, China;
2. School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2010-03-12 Published:2011-04-21

摘要/Abstract

摘要：

利用两个矩阵的奇异值分解(P-SVD)以及广义逆矩阵的性质,研究了两个矩阵乘积的｛1,2,3｝-逆和｛1,2,4｝-逆的反序律,得到了(AB)｛1,2,3｝⊆B｛1,2,3｝A｛1,2,3｝以及(AB)｛1,2,4｝⊆B｛1,2,4｝A｛1,2,4｝成立的充要条件,并获得了(AB)｛1,2,3｝=B｛1,2,3｝A｛1,2,3｝以及(AB)｛1,2,4｝=B｛1,2,4｝A｛1,2,4｝的等价条件。

关键词: 逆序律;广义逆;奇异值分值

Abstract:

The reverse order laws for ｛1,2,3｝-inverse and ｛1,2,4｝-inverse of product of two matrices have been studied by applying the product singular value decomposition P-SVD and the characters of generalized inverse. The necessary and sufficient conditions of (AB)｛1,2,3｝⊆B｛1,2,3｝A｛1,2,3｝ and (AB)｛1,2,4｝⊆B｛1,2,4｝A｛1,2,4｝are obtained. Then equivalent conditions of (AB)｛1,2,3｝=B｛1,2,3｝A｛1,2,3｝ and (AB)｛1,2,4｝=B｛1,2,4｝A｛1,2,4｝ are obtained.

Key words: reverse order law; Generalized inverse; P-SVD

张凤霞1,李莹1,2,赵建立1. 两个矩阵乘积的｛1,2,3｝-逆和｛1,2,4｝-逆的反序律[J]. J4, 2011, 46(4): 78-81.

ZHANG Feng-xia1, LI Ying1,2, ZHAO Jian-li1. The reverse order law for ｛1,2,3｝-inverse and ｛1,2,4｝-inverse of products of two matrices[J]. J4, 2011, 46(4): 78-81.

参考文献

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed