ABSTRACT

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.

中文翻译：

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一些广义可逆算子的结构和性质

摘要

在本文中，我们分析了各种广义逆的矩阵结构，提出了它们的适用范围，并建立了它们与特定投影的关系。作为应用，提出了几个核心-EP（Range-Hermitian）关系，星序，尖锐阶和MP-核心-EP（MPCEP）关系的等效条件。这些订单或关系之间的关系已建立。另外，我们介绍了核心-EP可逆算符满足逆序定律的一些条件。