| 复半正定矩阵乘积的半正定性 |
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| 引用本文： | 万文婷.复半正定矩阵乘积的半正定性[J].荆门职业技术学院学报,2010,25(9):41-43. |
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| 作者姓名： | 万文婷 |
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| 作者单位： | 荆楚理工学院,数理学院,湖北,荆门,448000 |
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| 摘 要： | 复半正定矩阵是半正定Hermite矩阵的推广。本文利用矩阵的特征值,讨论了复半正定矩阵乘积的半正定性,给出了两个复半正定矩阵的乘积仍是复半正定矩阵的几个充分条件以及两个特殊的复半正定矩阵的乘积仍是复半正定矩阵的充要条件。
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| 关 键 词： | 复半正定矩阵 半正定Hermite矩阵 矩阵的乘积 特征值 |
The Positive Semidefiniteness of Product of Complex Positive Semidefinite Matrices |
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| WAN Wen-ting.The Positive Semidefiniteness of Product of Complex Positive Semidefinite Matrices[J].Journal of Jingmen Vocational Technical College,2010,25(9):41-43. |
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| Authors: | WAN Wen-ting |
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| Institution: | WAN Wen-ting(School of Mathematics and Physics,Jingchu University of Technology,Jingmen,Hubei,448000,China) |
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| Abstract: | Complex positive semidefinite matrix is the promotion of the positive semidefinite Hermitian matrix.Using eigenvalue of matrices,the author discusses the positive semidefiniteness of product of complex positive semidefinite matrices,then gives a number of sufficient conditions on the positive semidefiniteness of the matrix product of two complex positive semidefinite matrices,and also provides some necessary and sufficient conditions on the positive semidefiniteness of the matrix product of two special complex positive semidefinite matrices. |
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| Keywords: | complex positive semidefinite matrix positive semidefinite Hermitian matrix product of matrices eigenvalue |
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