Imbedding conditions for normal matrices

When can an (n-k)×(n-k) normal matrix B be imbedded in an n×n normal matrix A? This question was studied for the first time 50 years ago by Ky Fan and Gordon Pall, who gave the complete answer in the case k=1. Since then, a few authors obtained additional results. In this note, we show how an approach inspired by the Hermitian case can throw some light on the problem.