Abstract
For any square matrix $A$, it is proved that minimal rank weak Drazin inverses (Campbell and Meyer, 1978) of $A$ coincide with outer inverses of $A$ with range $\mathcal{R}(A^{k})$, where $k$ is the index of $A$. It is shown that the minimal rank weak Drazin inverse behaves very much like the Drazin inverse, and many generalized inverses such as the core-EP inverse and the DMP inverse are its special cases.
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