Further properties and representations of the W-weighted m-weak group inverse
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909536442384384 |
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| author | Gao, Jiale Wang, Qing-Wen Zuo, Kezheng |
| author_facet | Gao, Jiale Wang, Qing-Wen Zuo, Kezheng |
| contents | The purpose of this paper is to explore more properties and representations of the W-weighted m-weak group (in short, W-m-WG) inverse. We first explore an interesting relation between two projectors with respect to the W-m-WG inverse. Then, the W-m-WG inverse is represented by various generalized inverses including W-weighted Drazin inverse, W-weighted weak group inverse, W-weighted core inverse, etc. We also give three concise explicit expressions for the W-m-WG inverse. Moreover, a canonical form of the W-m-WG inverse is presented in terms of the singular value decomposition. Finally, several numerical examples are designed to illustrate some results given in the paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_10704 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Further properties and representations of the W-weighted m-weak group inverse Gao, Jiale Wang, Qing-Wen Zuo, Kezheng Rings and Algebras Functional Analysis 15A09, 15A24 The purpose of this paper is to explore more properties and representations of the W-weighted m-weak group (in short, W-m-WG) inverse. We first explore an interesting relation between two projectors with respect to the W-m-WG inverse. Then, the W-m-WG inverse is represented by various generalized inverses including W-weighted Drazin inverse, W-weighted weak group inverse, W-weighted core inverse, etc. We also give three concise explicit expressions for the W-m-WG inverse. Moreover, a canonical form of the W-m-WG inverse is presented in terms of the singular value decomposition. Finally, several numerical examples are designed to illustrate some results given in the paper. |
| title | Further properties and representations of the W-weighted m-weak group inverse |
| topic | Rings and Algebras Functional Analysis 15A09, 15A24 |
| url | https://arxiv.org/abs/2312.10704 |