论文信息 - Similarity preserving linear maps on matrices

Similarity preserving linear maps on matrices

Abstract We determine all similarity preserving linear maps on the space of n x n complex matrices and all unitary equivalence preserving linear maps on the space of n x n Hermitian matrices. (Sub)majorization preserving linear maps on Hermitian matrices are also determined.

Fumio Hiai | F. Hiai

[1] Marvin Marcus,et al. Transformations on tensor product spaces , 1959 .

[2] I. Olkin,et al. Inequalities: Theory of Majorization and Its Applications , 1980 .

[3] G. Chan,et al. Linear transformations on symmetric matrices that preserve commutativity , 1982 .

[4] Rajendra Bhatia,et al. ANALYSIS OF SPECTRAL VARIATION AND SOME INEQUALITIES , 1982 .

[5] V. Arnold. ON MATRICES DEPENDING ON PARAMETERS , 1971 .

[6] O. Bratteli. Operator Algebras And Quantum Statistical Mechanics , 1979 .

[7] Linear Maps Preserving Commutativity , 1987 .

[8] Linear Operators Preserving The Real Symplectic Group , 1975, Canadian Journal of Mathematics.

[9] K. Chong. Spectral order preserving matrices and Muirhead’s theorem , 1974 .

[10] 安藤毅. Majorization, doubly stochastic matrices and comparison of eigenvalues , 1982 .

[11] LeRoy B. Beasley. Linear transformations on matrices: the invariance of rank k matrices , 1970 .

[12] M. Marcus. Linear transformations on matrices , 1971 .

[13] Commutativity-preserving operators on symmetric matrices , 1984 .

[14] G. Chan,et al. Linear transformations on symmetric matrices II , 1979 .