Variation in Jordan structure under congruence: The nilpotent case (Q947662)

The authors determine all possible nilpotent Jordan structures occurring in each congruence class. This is done by imposing two constraints: a fixed number of Jordan blocks, determined by the rank of the class, and a minimum number of one-by-one blocks, determined by the dimension of the intersection of the null spaces of \(A\) and \(A^*\), for \(A\) a representative of the class. An important tool, of independent interest, is a unitary version of the Jordan normal form.