Simple polynomial equations over (mxm)-matrices
Vitalij A. Chatyrko, Alexandre Karassev

TL;DR
This paper studies solutions to polynomial matrix equations over 3x3 real matrices, describing the solution set and its dimension, providing insights into the structure of such equations for matrices of size at least 3.
Contribution
It characterizes the solution set of polynomial equations over (mxm)-matrices for m ≥ 3, especially detailing the case m=3 and computing the dimension of the solution set.
Findings
Solution set for m=3 described explicitly.
Dimension of the solution set calculated for m=3.
Provides a topological description of solutions in Euclidean space.
Abstract
Let be any integer . We consider the polynomial equation over -matrices with the real entries, where is the identity matrix, is the null matrix, for each and . We discuss its solution set supplied with the natural Euclidean topology. In particular, we describe the solution set for and calculate its dimension.
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Taxonomy
TopicsMatrix Theory and Algorithms · Polynomial and algebraic computation · Advanced Optimization Algorithms Research
