On the number of unitary similarity classes in a C-S equivalence class: the normal case

Abstract

A matrix B∈ M n is C-S equivalent to A∈ M n if B is both congruent and similar to A. We study the question of how many unitary similarity classes lie in the C-S equivalence class of a given matrix A. The case of singular A is reduced to the nonsingular case in general, and we give a complete solution to the problem in case A is normal. Differences between the normal and general cases are noted.