Article
| Title: | New results on the $W$-core inverse of matrices (English) |
| Author: | Chen, Mingyue |
| Author: | Zhu, Huihui |
| Author: | Dong, Bing |
| Author: | Mosić, Dijana |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 2 |
| Year: | 2026 |
| Pages: | 591-606 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $A$, $W$ be two $n\times n$ complex matrices. We present the expression of the $W$-core inverse of $A$ by Hartwig and Spindelböck's decompositions and full rank decompositions. It is also proved that $A$ is $W$-core invertible if and only if $A$ is right $W$-core invertible. This equivalence may not be true in a general $*$-ring, see H. H. Zhu, L. Y. Wu, D. Mosić (2023). Then, several results for the reverse order law of the $W$-core inverse are given. Another accomplishment of this paper is to establish some perturbation properties and perturbation bounds for the $W$-core inverse, under some conditions. Finally, the necessary and sufficient condition for the continuity of the $W$-core inverse is derived. (English) |
| Keyword: | $W$-core inverse |
| Keyword: | reverse order law |
| Keyword: | perturbation |
| Keyword: | spectral norm |
| MSC: | 15A03 |
| MSC: | 15A09 |
| MSC: | 15A12 |
| DOI: | 10.21136/CMJ.2026.0355-25 |
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| Date available: | 2026-05-22T11:22:54Z |
| Last updated: | 2026-05-25 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153651 |
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