Companion matrices as sums of $p$-potent and nilpotent matrices
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918124281921536 |
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| author | Pojar, Andrada |
| author_facet | Pojar, Andrada |
| contents | We prove that, over a field $\mathbb{F}$ of odd characteristic $p$, a companion matrix $C$ is the sum of $E$ and $N$, with $E$ $p$-potent (i.e. $E^p = E$,) and $N$ nilpotent, if and only if the trace of $C$ is an integer multiple of unity of $\mathbb{F}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Companion matrices as sums of $p$-potent and nilpotent matrices Pojar, Andrada Rings and Algebras We prove that, over a field $\mathbb{F}$ of odd characteristic $p$, a companion matrix $C$ is the sum of $E$ and $N$, with $E$ $p$-potent (i.e. $E^p = E$,) and $N$ nilpotent, if and only if the trace of $C$ is an integer multiple of unity of $\mathbb{F}$. |
| title | Companion matrices as sums of $p$-potent and nilpotent matrices |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2508.09276 |