English

New characterizations of weak CMP inverses

Rings and Algebras 2025-09-11 v1

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)(e,f)-inverses.

Keywords

Cite

@article{arxiv.2509.08229,
  title  = {New characterizations of weak CMP inverses},
  author = {Shuxian Xu and Jianlong Chen},
  journal= {arXiv preprint arXiv:2509.08229},
  year   = {2025}
}
R2 v1 2026-07-01T05:29:24.253Z