The structures and properties of some generalized invertible operators
Xiaoli Deng, Chujian Lin, Chunyuan Deng · Linear and Multilinear Algebra · 2020
In this paper, we analyse the matrix structures of various generalized inverses, suggest their applicable scopes and build their relationships with particular projections. As applications, several equivalent conditions for core–EP (Range-Hermitian) relation, star order, sharp order and MP–Core–EP (MPCEP) relation are presented. The relationships among these orders or relations are built. In addition, we introduce some conditions for which the core–EP invertible operators satisfy the reverse order law.