Simple polynomial equations over (m x m)-matrices

Abstract

[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.