ABSTRACT

This paper introduces and investigates a new class of generalized inverses, called GDMP-inverses (and their duals), as a generalization of DMP-inverses. GDMP-inverses are defined from G-Drazin inverses and the Moore-Penrose inverse of a complex square matrix. In contrast to most other generalized inverses, GDMP-inverses are not only outer inverses but also inner inverses. Characterizations and representations of GDMP-inverses are obtained by means of the core-nilpotent and the Hartwig-Spindelböck decompositions.

中文翻译：

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矩阵的GDMP逆及其对偶

摘要

本文介绍并研究了一类新的广义逆，称为GDMP逆（及其对偶），作为DMP逆的泛化。GDMP逆是根据复杂方矩阵的G-Drazin逆和Moore-Penrose逆定义的。与大多数其他广义逆相反，GDMP逆不仅是外部逆，而且是内部逆。GDMP逆的表征和表示是通过核心幂等分解和Hartwig-Spindelböck分解获得的。