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arXiv · 2509.08229

New characterizations of weak CMP inverses

Shuxian Xu·Jianlong Chen
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Abstract

In 2025, Mosi\'{c} defined the weak CMP inverse utilizing a minimal rank weak Drazin inverse instead of the Drazin inverse. The weak CMP inverse is a new wider class of generalized inverses, of which the CMP and MPCEP inverse are particular cases. In this paper, we provide several expressions, along with a number of new characterizations and properties for the weak CMP inverse. Moreover, we investigate the relationships between the weak CMP inverse and some well-known generalized inverses, such as the Moore-Penrose inverse and weak MPD inverse. Finally, we show that the weak CMP inverse, weak MPD inverse and weak DMP inverse are all strong Bott-Duffin $(e,f)$-inverses.

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Shuxian Xu, Jianlong Chen. 2025-09-10. New characterizations of weak CMP inverses. https://arxiv.org/abs/2509.08229

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