复半正定矩阵乘积的半正定性  

The Positive Semidefiniteness of Product of Complex Positive Semidefinite Matrices

作　　者：万文婷[1] 

机构地区：[1]荆楚理工学院数理学院,湖北荆门448000

出　　处：《荆楚理工学院学报》2010年第9期41-43,共3页Journal of Jingchu University of Technology

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。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.

关 键 词：复半正定矩阵 半正定Hermite矩阵 矩阵的乘积 特征值 

分 类 号：O151.21[理学—数学]