环上矩阵的加权Moore-Penrose逆

J4 ›› 2011, Vol. 46 ›› Issue (12): 55-59.

环上矩阵的加权Moore-Penrose逆

袁玩贵,孔祥智

江南大学理学院, 江苏无锡 214122

出版日期:2011-12-20 发布日期:2011-12-24
作者简介:袁玩贵(1974- ),男,硕士,讲师,研究方向为代数. Email:ywg-602@163.com

Weighted Moore-Penrose inverses on rings

YUAN Wan-gui, KONG Xiang-zhi

School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China

Online:2011-12-20 Published:2011-12-24

摘要/Abstract

摘要：

在正则环上将加权Moore-Penrose逆的权数矩阵M,N推广到任意矩阵,得到了M,N为任意矩阵时,加权Moore-Penrose逆存在的充要条件,并构造出矩阵A的｛1,3M｝、｛1,4N｝、｛1,2,3M｝、｛1,3M,4N｝和｛1,2,3M,4N｝的全部元素。

关键词: 广义逆;加权Moore-Penrose逆;矩阵

Abstract:

Assuming that M, N are arbitrary matrices on rings, it is discussed that the necessary and sufficient conditions of the weighted Moore-Penrose inverses with respect to M,N for existences. In addition, it is found that the all solutions of A｛1,3M｝, A｛1,4N｝, A｛1,2,3M｝, A｛1,3M,4N｝ and A｛1,2,3M,4N｝.

Key words: generalized inverse; weighted Moore-Penrose inverses; matrix

袁玩贵,孔祥智. 环上矩阵的加权Moore-Penrose逆[J]. J4, 2011, 46(12): 55-59.

YUAN Wan-gui, KONG Xiang-zhi. Weighted Moore-Penrose inverses on rings[J]. J4, 2011, 46(12): 55-59.

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