Preservers of condition spectra and pseudo spectra of Hermitian matrix Jordan products

Abstract

. Let H n be the real space of n × n complex Hermitian matrices. Complete descriptions are given of the maps of H n leaving invariant the pseudo spectral radius or the condition spectral radius of Jordan product of matrices. As application, maps on H n that preserve the condition spectrum of Jordan product of matrices are classi fi ed. Mathematics subject classi fi cation (2020): 47B49, 47A10, 47A25.