| 广义正定矩阵的特殊乘积 |
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| 引用本文： | 焦争呜. 广义正定矩阵的特殊乘积[J]. 河南师范大学学报(自然科学版), 1992, 20(3): 23-26 |
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| 作者姓名： | 焦争呜 |
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| 作者单位： | 河南师范大学数学系 |
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| 摘 要： | 设H_n={A|A∈C~(n×n),A~*=A,且对所有的0≠x∈C~n,(x,Ax)=x~*Ax>0}。C_n={A|A∈C~(h×n),且对所有0≠x∈C~n,(x,Ax)= x~*Ax>0}。本文证明了下面事实:如果A∈H_n,B∈G_n,那么A(?)B,B(?)A和A·B∈G_n,同时我们有反例来说明如果A,B∈G_n,那么A(?)B,A·B∈G_n是不正确的。
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| 关 键 词： | 广义正定矩阵 广义对角矩阵 矩阵Kronccker乘积和Hadamard乘积 |
SPECLAL PROOUCTS OF POSITIVE DEFINITE MATRICES |
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| Jiao Zhengming. SPECLAL PROOUCTS OF POSITIVE DEFINITE MATRICES[J]. Journal of Henan Normal University(Natural Science), 1992, 20(3): 23-26 |
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| Authors: | Jiao Zhengming |
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| Affiliation: | Jiao Zhengming Department of Mathematics |
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| Abstract: | Let H_n= {A|A∈C~(n×n),, A = A and (x, Ax)=x Ax>o for all 0≠x∈C~n} G_n = {A|A∈C~(n×n), and (x, Ax) =x Ax>0 for all 0≠x∈C~n}. It is shown that if A∈H_n, B∈G_n, then A×B. B×A and A·B∈G_n. We also findcounterexamples to show that it is not true that if A, B∈G_n, then A×B, A·B∈G_n. |
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| Keywords: | Generalized positive definite matrix Generalized diagonol matrix. Kronecker Product Hadamard product |
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