New characterizations of weak CMP inverses
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916944339271680 |
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| author | Xu, Shuxian Chen, Jianlong |
| author_facet | Xu, Shuxian Chen, Jianlong |
| contents | In 2025, Mosić defined the weak CMP inverse utilizing a minimal rank weak Drazin inverse instead of the Drazin inverse. The weak CMP inverse is a new wider class of generalized inverses, of which the CMP and MPCEP inverse are particular cases. In this paper, we provide several expressions, along with a number of new characterizations and properties for the weak CMP inverse. Moreover, we investigate the relationships between the weak CMP inverse and some well-known generalized inverses, such as the Moore-Penrose inverse and weak MPD inverse. Finally, we show that the weak CMP inverse, weak MPD inverse and weak DMP inverse are all strong Bott-Duffin $(e,f)$-inverses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New characterizations of weak CMP inverses Xu, Shuxian Chen, Jianlong Rings and Algebras In 2025, Mosić defined the weak CMP inverse utilizing a minimal rank weak Drazin inverse instead of the Drazin inverse. The weak CMP inverse is a new wider class of generalized inverses, of which the CMP and MPCEP inverse are particular cases. In this paper, we provide several expressions, along with a number of new characterizations and properties for the weak CMP inverse. Moreover, we investigate the relationships between the weak CMP inverse and some well-known generalized inverses, such as the Moore-Penrose inverse and weak MPD inverse. Finally, we show that the weak CMP inverse, weak MPD inverse and weak DMP inverse are all strong Bott-Duffin $(e,f)$-inverses. |
| title | New characterizations of weak CMP inverses |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2509.08229 |