2025/09/10 by Xu, Shuxian, Chen, Jianlong
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2509.08229
In 2025, Mosić 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.