On Normal and Binormal Matrices.

The problem discussed is how to obtain a normal matrix from a binormal one and, conversely, a binormal matrix from a normal one via the right multiplication on a suitable unitary matrix. Let be a normal matrix badly conditioned with respect to inversion, that is, having a large condition number . We show that, among the binormal matrices that can be obtained from , there is a matrix whose eigenvalues have individual condition numbers of order . [ABSTRACT FROM AUTHOR]