This paper introduces a new class of generalized inverses for square matrices: core-EP G-Drazin (CEPGD) inverse. The CEPGD inverse is not unique and defined as a proper composition of the core-EP and the G-Drazin inverse. Representations of CEPGD inverses related to the core-nilpotent decomposition and the Hartwig–Spindelböck decomposition are established. The existence of CEPGD inverses as well as a few characterizations and representations of this inverse are discussed. In addition, we consider some additional properties of the CEPGD inverses through an induced binary relation.

中文翻译：

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方阵的 CEPGD 逆矩阵

本文介绍了一类新的方阵广义逆：core-EP G-Drazin (CEPGD) 逆。CEPGD 逆并不是唯一的，并且被定义为 core-EP 和 G-Drazin 逆的适当组合。建立了与核幂零分解和 Hartwig-Spindelböck 分解相关的 CEPGD 逆的表示。讨论了 CEPGD 逆的存在以及该逆的一些特征和表示。此外，我们还通过归纳二元关系考虑了 CEPGD 逆的一些附加属性。