Abstract
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.
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Xiao-min Tang received his Dr from Harbin Institute of Technology. Since 1999 he has been at the Heilongjiang University. In 2004, he received an Associate Professor from Heilongjiang Education Committee. His research interests center on the theory of matrix algebra and its applications.
Chong-guang Cao received his MS from Northeastern Normal University. Since 1981 he has been at the Heilongjiang University. In 1992, he received a Professor from Heilongjiang Education Committee. His research intrests center on the theory of classical group and matrix algebra.
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Tang, XM., Cao, CG. Linear maps preserving pairs of Hermitian matrices on which the rank is additive and applications. JAMC 19, 253–260 (2005). https://doi.org/10.1007/BF02935803
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DOI: https://doi.org/10.1007/BF02935803