Kr. Driessel et Ws. So, LINEAR-OPERATORS ON MATRICES - PRESERVING SPECTRUM AND DISPLACEMENT STRUCTURE, SIAM journal on matrix analysis and applications, 16(2), 1995, pp. 488-501
In this paper we characterize those linear operators on general matric
es that preserve singular values and displacement rank. We also charac
terize those linear operators on Hermitian matrices that preserve eige
nvalues and displacement inertia.