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arXiv · 2507.07085

Simple polynomial equations over (mxm)-matrices

Vitalij A. Chatyrko·Alexandre Karassev
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Abstract

Let $m$ be any integer $\geq 3$. 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 $(m \times m)$-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 $n \geq 1$. We discuss its solution set $S$ supplied with the natural Euclidean topology. In particular, we describe the solution set $S$ for $m=3$ and calculate its dimension.

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Vitalij A. Chatyrko, Alexandre Karassev. 2025-07-09. Simple polynomial equations over (mxm)-matrices. https://arxiv.org/abs/2507.07085

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