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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.24285 |
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| _version_ | 1866911347103498240 |
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| author | Senapati, Rajesh Nandi, Ashish Kumar |
| author_facet | Senapati, Rajesh Nandi, Ashish Kumar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Characterizations of W-weighted DMP and MPD Inverses Senapati, Rajesh Nandi, Ashish Kumar Rings and Algebras 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. |
| title | On Characterizations of W-weighted DMP and MPD Inverses |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2512.24285 |