Imbedding conditions for normal matrices

Abstract

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.

Block normal matrices and Gershgorin-type discs

“…If, additionally, the matrix A is normal, one can estimate real and imaginary parts of eigenvalues of A in terms of eigenvalues of diagonal blocks A kk ; see also [8] where interesting analogue of min-max theorem for normal matrices was presented.…”