线性变换的群逆

本文研究任意维数向量空间的任意线性变换A的群逆。首先给出线性变换A有群逆的一些新的充要条件,其次给出无限维向量空间的线性变换A满足A~＃=A~+的充要条件,最后对有限维线性变换或方阵A满足A~＃=A~+给出一些新的充要条件。

THE GROUP INVERSE OF A LINEAR TRANSFORMATION

In this paper we investigate the group inverse of a linear transformation A of a dimensional-free vecter space.We first give more new necessary and sufficient conditions for the transformation A to have a group inverse.We also establish the necessary and sufficient conditions for a linear transfor- mation A of an infinite dimensional vector space to have A~#=A~+,At last we give more new sets of this kind of conditions for a square matrix A.