环上矩阵的加权广义逆

摘要/Abstract

摘要：

该文从另一方面给出了 Hartwig R E^[27]提出的公开问题的解答. 设R是带有对合*的任意环, 作者定义了环R上的一种新的加权广义逆, 记为A⁺_P, _Q,并给出了A⁺_{P, Q}存在的充要条件. 同时, 得到了一些重要的性质.

关键词: 环, 矩阵, 加权广义逆, 满单分解

Abstract:

In this paper, we give a new kind of answer from another aspect to an open problem posed by Hartwig R E^[27].Let R be an arbitrary ring with involution *. We define a new type of the weighted generalized inverse of matrices over R, denoted by A⁺_{P, Q}, and give the necessary and sufficient conditions for the existence of A⁺_{P, Q}. And several expressions of A⁺_{P, Q} are also given. Meanwhile, some important properties are obtained.

Key words: Ring, Matrices, Weighted generalized inverse, Epic-monic factorization

中图分类号:

15A09

廖祖华, 黄昱, 易丽华. 环上矩阵的加权广义逆[J]. 数学物理学报, 2010, 30(3): 708-717.

LIAO Zu-Hua, HUANG Yu, YI Li-Hua. The Weighted Generalized Inverses of Matrices over Rings[J]. Acta mathematica scientia,Series A, 2010, 30(3): 708-717.

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