Simple polynomial equations over (m x m)-matrices

[EN] Let m be any integer ? 3 . We consider the polynomial equation Xn+an-1·Xn-1+···+a1·X+a0·I=O,over (m x m)-matrices X with the real entries, where I is the identity matrix, O is the null matrix, ai ? ? for each i and n ? 1. We discuss its solution set S supplied with the natural Euclidean topolog...

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Bibliographic Details
Authors: Tjatyrko, Vitalij, Karassev, Alexandre
Format: article
Publication Date:2026
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:dnet:riunet______::3f1b72f56eac4cc1dde1967325c8dc78
Online Access:https://riunet.upv.es/handle/10251/235812
Access Level:Open access
Keyword:Polynomial equations over matrices
Matrix algebra
Covering dimension
Description
Summary:[EN] Let m be any integer ? 3 . We consider the polynomial equation Xn+an-1·Xn-1+···+a1·X+a0·I=O,over (m x m)-matrices X with the real entries, where I is the identity matrix, O is the null matrix, ai ? ? for each i and n ? 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.