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arXiv · 2512.24285

On Characterizations of W-weighted DMP and MPD Inverses

Rajesh Senapati·Ashish Kumar Nandi
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Abstract

Recently, the weak Drazin inverse and its characterization have been crucial studies for matrices of index k. In this article, we have revisited W-weighted DMP and MPD inverses and constructed a general class of unique solutions to certain matrix equations. Moreover, we have generalized the W-weighted Drazin inverse of Meng, 2017 using the minimal rank Wweighted weak Drazin inverse. In addition to that, we have derived several equivalent properties of W-weighted DMP and MPD inverses for minimal rank W-weighted weak Drazin inverse of rectangular matrices. Furthermore, some projection-based results are discussed for the characterization of minimal rank W-weighted Drazin inverse, along with some new expressions that are derived for MPD and DMP inverses. Thereby, we have elaborated certain expressions of the perturbation formula for W-weighted weak MPD and DMP inverses. As an application, we establish the reverse and forward order laws using the W-weighted weak Drazin inverse and the minimal rank W-weighted weak Drazin inverse, and apply these results to solve certain matrix equation.

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Rajesh Senapati, Ashish Kumar Nandi. 2025-12-30. On Characterizations of W-weighted DMP and MPD Inverses. https://arxiv.org/abs/2512.24285

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