On the number of unitary similarity classes in a C-S equivalence class: the normal case (Q1601630)

A matrix \(B\in{\mathcal M}_n\) is \(C-S\) equivalent to \(A\in{\mathcal M}_n\) if \(B\) is both congruent and similar to \(A\). The paper studies 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 a complete solution to the problem in case \(A\) is normal is given. Differences between the normal and general cases are noted.