On normal forms for the similarity classes of matrices and pairs of matrices

2025/02/15 by Bongartz, Klaus
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2502.10926

Abstract

We answer two questions posed 1998 in the book 'Arnolds problems'. First, over any field k there is a representative system for the similarity classes of nxn-matrices which is a finite disjoint union of affine subspaces. And second, for n>1 an analogous statement fails for pairs of nxn-matrices over any algebraically closed field of characteristic 0.

Related

• Normal form of m-by-n-by-2 matrices for equivalence
• Representatives of similarity classes of matrices over PIDs corresponding to ideal classes
• On the diagonal of the matrices in a similarity class
• Canonical forms for a class of pairs of commuting nilpotent matrices under simultaneous similarity
• The Deligne-Simpson Problem