The core-EP inverse: A numerical approach for its acute perturbation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911973728321536 |
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| author | Zhou, Mengmeng chen, Jianlong Thome, Nestor |
| author_facet | Zhou, Mengmeng chen, Jianlong Thome, Nestor |
| contents | This paper studies the concept of stable perturbation $B\in\mathbb{C}^{n\times n}$ for the core-EP inverse of a matrix $A\in\mathbb{C}^{n\times n}$ with index $k$. For a given stable perturbation $B$ of $A$, explicit expressions of its core-EP inverse $B^{\scriptsize\textcircled{\tiny $\dagger$}}$ and its projection at zero $B^π$ are presented. Then, the perturbation bounds of $\parallel B^{\scriptsize\textcircled{\tiny $\dagger$}}-A^{\scriptsize\textcircled{\tiny $\dagger$}}\parallel/\parallel A^{\scriptsize\textcircled{\tiny $\dagger$}}\parallel$ and $\parallel B^π-A^π\parallel$ are given provided that $B$ is a stable perturbation of $A$. In addition, we investigate the concept of acute perturbation of $A$. We give a perturbation analysis with respect to core-EP inverses. We provide a condition under which the acute perturbation coincides with the stable perturbation for core-EP inverses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21419 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The core-EP inverse: A numerical approach for its acute perturbation Zhou, Mengmeng chen, Jianlong Thome, Nestor Rings and Algebras 15A09, 65F20 This paper studies the concept of stable perturbation $B\in\mathbb{C}^{n\times n}$ for the core-EP inverse of a matrix $A\in\mathbb{C}^{n\times n}$ with index $k$. For a given stable perturbation $B$ of $A$, explicit expressions of its core-EP inverse $B^{\scriptsize\textcircled{\tiny $\dagger$}}$ and its projection at zero $B^π$ are presented. Then, the perturbation bounds of $\parallel B^{\scriptsize\textcircled{\tiny $\dagger$}}-A^{\scriptsize\textcircled{\tiny $\dagger$}}\parallel/\parallel A^{\scriptsize\textcircled{\tiny $\dagger$}}\parallel$ and $\parallel B^π-A^π\parallel$ are given provided that $B$ is a stable perturbation of $A$. In addition, we investigate the concept of acute perturbation of $A$. We give a perturbation analysis with respect to core-EP inverses. We provide a condition under which the acute perturbation coincides with the stable perturbation for core-EP inverses. |
| title | The core-EP inverse: A numerical approach for its acute perturbation |
| topic | Rings and Algebras 15A09, 65F20 |
| url | https://arxiv.org/abs/2407.21419 |