Hermite矩阵张量积空间上保持秩可加和秩和最小的线性映射
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摘要
在给定的集合上研究保持某种不变量的映射的问题被称为保持问题,该问题已成为矩阵理论中的一个核心研究领域.主要刻画了Hermite矩阵张量积空间■保持秩可加和秩和最小的线性映射.
The problems of characterizing mappings that preserve certain invariant on given sets are called the preserving problems, which have become one of the core research areas in matrix theory. In this paper, linear maps that preserve rank-additivity and rank-sum-minimal on tensor products of Hermite matrices spaces ■are characterized respectively.
The problems of characterizing mappings that preserve certain invariant on given sets are called the preserving problems, which have become one of the core research areas in matrix theory. In this paper, linear maps that preserve rank-additivity and rank-sum-minimal on tensor products of Hermite matrices spaces ■are characterized respectively.
引文
[1] Alexander Guterman. Linear Preservers for Matrix Inequalities and Partial Orderings[J]. Linear Algebra and its Applications, 2001, 331: 75-87.
[2] LeRoy B Beasley, Sang Gu Lee, Seok Zun Song. Linear Operators that Preserve Pairs of Matrices which Satisfy Extreme Rank Properties[J]. Linear Algebra and its Applications, 2002, 50: 263-272.
[3] Zhang Xian. Linear Operators that Preserve Pairs of Matrices which Satisfy Extreme Rank Properties-A Supplementary Version[J]. Linear Algebra and its Applications, 2003, 375: 283-290.
[4] Zhang Xian. Linear Preservers of Rank-sum-maximum,Rank,Rank-subtractivity,and Rank-sum-minimum on Symmetric Matrices[J]. Linear and Multilinear Algebra,2007, 53:153-165.
[5] Tang Xiao-min , Yang Ya-qin. Linear Preservers of Rank-additivity on the Spaces of Hermitian Matrices and their Applications[J]. 黑龙江大学自然科学学报, 2004,21(4):63-67.
[6] Fosner, Huang Z,et al. Linear Preservers and Quantum Information Science[J]. Linear and Multilinear Algebra, 2013, 61: 1377-1390.
[7] Yuting Ding , Ajda Fo, Jinli Xu etal. Linear Maps Preserving Determinant of Tensor Products of Hermitian Matrices[J]. Mathematical Analysis and Applications, 2017,446:1139-1152.
[8] Xu J, Zheng B. Linear Maps Preserving Tensor Products of Rank-one Hermitian Matrices[J]. Journal of the Australian Mathematical Society, 2015, 98:407-428.
[2] LeRoy B Beasley, Sang Gu Lee, Seok Zun Song. Linear Operators that Preserve Pairs of Matrices which Satisfy Extreme Rank Properties[J]. Linear Algebra and its Applications, 2002, 50: 263-272.
[3] Zhang Xian. Linear Operators that Preserve Pairs of Matrices which Satisfy Extreme Rank Properties-A Supplementary Version[J]. Linear Algebra and its Applications, 2003, 375: 283-290.
[4] Zhang Xian. Linear Preservers of Rank-sum-maximum,Rank,Rank-subtractivity,and Rank-sum-minimum on Symmetric Matrices[J]. Linear and Multilinear Algebra,2007, 53:153-165.
[5] Tang Xiao-min , Yang Ya-qin. Linear Preservers of Rank-additivity on the Spaces of Hermitian Matrices and their Applications[J]. 黑龙江大学自然科学学报, 2004,21(4):63-67.
[6] Fosner, Huang Z,et al. Linear Preservers and Quantum Information Science[J]. Linear and Multilinear Algebra, 2013, 61: 1377-1390.
[7] Yuting Ding , Ajda Fo, Jinli Xu etal. Linear Maps Preserving Determinant of Tensor Products of Hermitian Matrices[J]. Mathematical Analysis and Applications, 2017,446:1139-1152.
[8] Xu J, Zheng B. Linear Maps Preserving Tensor Products of Rank-one Hermitian Matrices[J]. Journal of the Australian Mathematical Society, 2015, 98:407-428.