This paper reveals the relationship of minimal rank weak Drazin inverses in matrices, suggesting broader applications in linear algebra.
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.
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Wu et al. (2025) studied this question.
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