| Mn上保持矩阵自Jordan积的线性映射 |
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| 引用本文： | 毛雁翎.Mn上保持矩阵自Jordan积的线性映射[J].纺织高校基础科学学报,2011(4):517-520. |
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| 作者姓名： | 毛雁翎 |
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| 作者单位： | 陕西师范大学数学与信息科学学院 |
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| 基金项目： | 国家自然科学基金资助项目(10971123) |
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| 摘 要： | 设Mn是复数域上n×n矩阵代数,Φ是Mn上的非零线性映射,则Φ保持自Jordan积,即(V)A∈Mn,都有Φ(A*(.)A)=Φ(A)*(.)Φ(A)当且仅当存在Mn中的酉矩阵U,使得Φ(X)=UXU*,(V)X∈Mn,或者Φ(X)=UXTU*,(V) X∈un,其中XT表示矩阵X的转置.
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| 关 键 词： | 线性映射 自Jordan积 保持映射 |
Linear maps preserving self-Jordan products of matrices on M_n |
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| MAO Yan-ling.Linear maps preserving self-Jordan products of matrices on M_n[J].Basic Sciences Journal of Textile Universities,2011(4):517-520. |
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| Authors: | MAO Yan-ling |
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| Affiliation: | MAO Yan-ling(College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China) |
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| Abstract: | Let Mn be the algebra of all n×n complex matrices.It is proved that a non-zero linear map Φ on Mn preserving the self-Jordan products,that is Φ(A* A)=Φ(A)*Φ(A) for all A∈Mn,if and only if there is a unitary matrix U in Mn such that Φ(X)=UXU*,X∈Mn,or Φ(X)=UXT U*,X∈Mn,where XT denotes the transpose of matrix X. |
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| Keywords: | linear maps self-Jordan products preserving maps |
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