环上矩阵的加权广义逆

The Weighted Generalized Inverses of Matrices over Rings

该文从另一方面给出了Hartwig R E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.

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