数学杂志2017，Vol.37Issue(5)：1013-1021,9.
线性空间中代数广义逆的最简表示
THE SIMPLEST EXPRESSION OF THE ALGEBRAIC GENERALIZED INVERSES IN LINEAR SPACES
摘要
Abstract
In this paper, the authors study the additivity and expression of algebraic generalized inverses from the view of pure algebra in the framework of linear space. Utilizing the algebraic direct sum decomposition of linear space, we first give the necessary and sufficient condition of the invertibility of I +AT+ and T+ = T+(I +AT+)?1. We also provide some necessary and sufficient conditions for T+ to have the simplest expression. As applications, we discuss the perturbation problem of generalized inverse in Banach space and Moore-Penrose inverse in Hilbert space, which extend and improve many recent results in this topic.关键词
代数广义逆/广义逆/Moore-Penrose逆/最简表示/线性空间Key words
algebraic generalized inverse/generalized inverse/Moore-Penrose inverse/the simplest expression/linear space分类
数理科学引用本文复制引用
郭志荣,黄强联,张莉..线性空间中代数广义逆的最简表示[J].数学杂志,2017,37(5):1013-1021,9.基金项目
国家自然科学基金资助(11771378 （）
11271316) （）
江苏省自然科学基金资助(BK20141271) （BK20141271）
扬州大学中青年学术带头人基金资助(2016zqn03). （2016zqn03）
