Jacobson’s lemma and Cline’s formula for minimal rank weak Drazin inverses
Cang Wu, Jianlong Chen, Yuanyuan Ke · Filomat · 2025
Minimal rank weak Drazin inverses of a square complex matrix M are solutions to the matrix equation XMk+1 = Mk with the minimal rank, covering a large class of generalized inverses. In this paper, minimal rank weak Drazin inverses of In-BA (resp. BA) are expressed in terms of that of Im-(resp. AB), where A and B are m ? n and n ? m complex matrices, respectively.