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

被引：1
作者：
Tang X.-M. [1 ]
Cao C.-G. [1 ]
机构：
[1] Department of Mathematics, Heilingjiang Univ., Harbin
来源：
Journal of Applied Mathematics and Computing | 2005年 / 19卷 / 1-2期
关键词：
Adjoint matrix; Hermitian matrix; Jordan homomorphism; Linear preserver; Rank-additive; Skew Hermitian matrix;
D O I：
10.1007/BF02935803
中图分类号：
学科分类号：
摘要：
Denote the set of n × n complex Hermitian matrices by Hn. A pair of n × n Hermitian matrices (A, B) is said to be rank-additive if rank (A + B) = rank A+rank B. We characterize the linear maps from Hn into itself that preserve the set of rank-additive pairs. As applications, the linear preservers of adjoint matrix on Hn and the Jordan homomorphisms of Hn are also given. The analogous problems on the skew Hermitian matrix space are considered. © 2005 Korean Society for Computational & Applied Mathematics and Korean SIGCAM.
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页码：253 / 260
页数：7
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  • [11] Ha K. C.(2004)Linear operators preserving adjoint matrix between matrix spaces J. Appl. Math. and Computing 14 115-122
  • [12] Petek T.(2004)Additive operators preserving rank-additivity on symmetrix matrix spaces Linear Algebra Appl. 380 185-198
  • [13] Šemrl P.(2003)Additive preservers of rank-additivity on the spaces of symmetric and alternate matrices Linear Algebra Appl. 380 283-290
  • [14] Šemrl P.(2004)Linear operators that preserve pairs of matrices which satisfy extreme rank properities-a supplementary version J. Appl. Math. and Computing 14 51-67
  • [15] Tang X. M.(undefined)The general Hermitian nonnegative-definete and positive-definite solutions to the matrix equation, GXG undefined undefined undefined-undefined
  • [16] Cao C. G.(undefined)+HY H undefined undefined undefined-undefined
  • [17] Zhang X.(undefined)=C undefined undefined undefined-undefined
  • [18] Tang X. M.(undefined)undefined undefined undefined undefined-undefined
  • [19] Tang X. M.(undefined)undefined undefined undefined undefined-undefined
  • [20] Cao C. G.(undefined)undefined undefined undefined undefined-undefined
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