Linear maps preserving pairs of Hermitian matrices on which the rank is additive and applications

摘要

Denote the set ofn×n complex Hermitian matrices byH n . A pair ofn×n Hermitian matrices (A, B) is said to be rank-additive if rank (A+B)=rankA+rankB. We characterize the linear maps fromH n into itself that preserve the set of rank-additive pairs. As applications, the linear preservers of adjoint matrix onH n and the Jordan homomorphisms ofH n are also given. The analogous problems on the skew Hermitian matrix space are considered.