Nonderogatory matrices as sums of $p$-potent and nilpotent matrices
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915446015393792 |
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| author | Pojar, Andrada |
| author_facet | Pojar, Andrada |
| contents | We prove that every nonderogatory matrix $A$ over a field of positive odd characteristic $p,$ that is sum of a $p$-potent matrix and a nilpotent matrix, has a decomposition $A=E+V,$ such that $E^p=E,$ and $V^3=0.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonderogatory matrices as sums of $p$-potent and nilpotent matrices Pojar, Andrada Rings and Algebras We prove that every nonderogatory matrix $A$ over a field of positive odd characteristic $p,$ that is sum of a $p$-potent matrix and a nilpotent matrix, has a decomposition $A=E+V,$ such that $E^p=E,$ and $V^3=0.$ |
| title | Nonderogatory matrices as sums of $p$-potent and nilpotent matrices |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2508.10079 |