| 矩阵张量积数值半径的一个不等式和一个等式 |
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| 引用本文： | 侯谦民. 矩阵张量积数值半径的一个不等式和一个等式[J]. 山西大学学报(自然科学版), 2007, 30(3) |
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| 作者姓名： | 侯谦民 |
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| 摘 要： | 借助矩阵张量积和矩阵数值半径的性质,证明了不等式r(A1(×)…(×)Ak)≥∏ki=1r(Ai)和等式r(A(×)B)=r(B(×)A),其中A1,…,Ak,A,B∈L(U).同时,举例说明了不等式r(k(×)A)≤rk(A)不成立.而当A1,…,Ak为正规阵时,有r(A1(×)…(×)Ak)=∏ks=1r(As).
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| 关 键 词： | 矩阵 数值半径 张量积 内积 向量 范数 |
One Inequality and An Equality on the Numerical Radius of Matrix Tensor Product |
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| HOU Qian-min. One Inequality and An Equality on the Numerical Radius of Matrix Tensor Product[J]. Journal of Shanxi University (Natural Science Edit, 2007, 30(3) |
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| Authors: | HOU Qian-min |
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| Abstract: | By using the properties of tensor product and numerical radius of matrix,for any n×n matrices A1,…,Ak∈L(U),the inequalityand for any two n×n matrices A,B∈L(U),the equality r(A(×)B)=r(B(×)A) is certainly hold are proved.Meanwhile the inequalities r(A(×)B)≤r(A)r(B) and r(A(×)A)≤r2(A) are all disappointingly incorrect through a simple illustration is demonstrated. |
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| Keywords: | Matrix numerical radius tensor product interior product vector norm |
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