| 矩阵乘积的特征值的估计 |
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| 引用本文： | 宋永忠.矩阵乘积的特征值的估计[J].南京师大学报,1994,17(2):10-13. |
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| 作者姓名： | 宋永忠 |
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| 作者单位： | 南京师范大学数学系 |
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| 摘 要： | 给出了两个正规阵或厄米阵之积的特征值的上、下界，给出了两个厄米半正定区之积的特征值的上、下界，还给出了两个矩阵之积的奇异值与原来两矩阵奇异值之间的关系．
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| 关 键 词： | 矩阵 特征值 奇异值 乘积 |
Estimations for the Eigenvalues of the Product of Matrices |
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| Song Yongzhong.Estimations for the Eigenvalues of the Product of Matrices[J].Journal of Nanjing Normal University(Natural Science Edition),1994,17(2):10-13. |
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| Authors: | Song Yongzhong |
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| Abstract: | For two radial matrices A and B an upper bound for the modulus of eigenvalues of AB in terms of those of A and B is obtained. Specially,we prove an upper and a lower bound for two normal or Hermitian matrices. When both A and B are positive semidefinite Hermitian matrices, better relations are proposed. At last,the relations between the singular values of AB and those of A and B are derived. |
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| Keywords: | Matrices Eigenvalue singular value Hermitian operator Positive definite matrices |
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