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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.07689 |
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| _version_ | 1866915333460197376 |
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| author | Chatyrko, Vitalij A. Karassev, Alexandre |
| author_facet | Chatyrko, Vitalij A. Karassev, Alexandre |
| contents | We consider the polynomial equation $$X^n + a_{n-1}\cdot X^{n-1} + \dots + a_1 \cdot X + a_0 \cdot I = O,$$ over $(2 \times 2)$-matrices $X$ with the real entries, where $I$ is the identity matrix, $O$ is the null matrix, $a_i \in \mathbb R$ for each $i$ and $n \geq 2$. We discuss its solution set $S$ supplied with the natural Euclidean topology. We completely describe $S$. We also show that $\dim S =2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple polynomial equations over $(2 \times 2)$-matrices Chatyrko, Vitalij A. Karassev, Alexandre Rings and Algebras General Topology 15A24, 54F45 (Primary), 15B30 (Secondary) We consider the polynomial equation $$X^n + a_{n-1}\cdot X^{n-1} + \dots + a_1 \cdot X + a_0 \cdot I = O,$$ over $(2 \times 2)$-matrices $X$ with the real entries, where $I$ is the identity matrix, $O$ is the null matrix, $a_i \in \mathbb R$ for each $i$ and $n \geq 2$. We discuss its solution set $S$ supplied with the natural Euclidean topology. We completely describe $S$. We also show that $\dim S =2.$ |
| title | Simple polynomial equations over $(2 \times 2)$-matrices |
| topic | Rings and Algebras General Topology 15A24, 54F45 (Primary), 15B30 (Secondary) |
| url | https://arxiv.org/abs/2506.07689 |