| 厄尔米特矩阵空间上秩可加线性保持及其应用 |
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| 引用本文： | 唐孝敏,杨雅琴. 厄尔米特矩阵空间上秩可加线性保持及其应用[J]. 黑龙江大学自然科学学报, 2004, 21(4): 63-67 |
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| 作者姓名： | 唐孝敏 杨雅琴 |
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| 作者单位： | 黑龙江大学,数学科学学院,黑龙江,哈尔滨,150080;黑龙江大学,数学科学学院,黑龙江,哈尔滨,150080 |
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| 基金项目： | Supported by NSF of Heilongjiang Province (A01-07)，the Fund of Heilongjiang Education Committee forOverseas Scholars ( 1054HQ004) |
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| 摘 要： | 以Hn记n×n复厄尔米特矩阵集合.刻划了Hn上秩可加线性保持.Hn对于运算加法(A,B)→A+B,乘法(A,B)→A·B=ABA和纯量乘法(c,A)→cA,其中A,B∈Hn及c∈R(实数域),形成一个非结合代数.给出了这个非结合代数的自同构.
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| 关 键 词： | 线性保持问题 自同构 厄尔米特矩阵 秩 |
Linear preservers of rank-additivity on the spaces of Hermitian matrices and their applications |
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| TANG Xiao-min,YANG Ya-qin. Linear preservers of rank-additivity on the spaces of Hermitian matrices and their applications[J]. Journal of Natural Science of Heilongjiang University, 2004, 21(4): 63-67 |
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| Authors: | TANG Xiao-min YANG Ya-qin |
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| Abstract: | Denote the set of n × n complex Hermitian matrices by Hn. The bijective linear preservers of rank-additivity on Hn are characterized. The set Hn forms a non-associative algebra with respect to the addition (A, B) → A + B, the multiplication (A, B) → A. B = ABA and the scalar multiplication (c, A) → cA where A, B ∈ Hn and c ∈ R(the real number field). The forms of any automorphism of the non-associative algebra are also given. |
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| Keywords: | linear preserver automorphism Hermitian matrix rank |
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