有关复正定矩阵的性质  

On the properties of the complex positive definite matrix

作　　者：郭华[1] 张晓翠[1] 

机构地区：[1]重庆工商大学理学院,重庆400067

出　　处：《重庆工商大学学报（自然科学版）》2004年第6期533-536,共4页Journal of Chongqing Technology and Business University:Natural Science Edition

摘　　要：从复矩阵的运算性质、矩阵为复正定矩阵的一些充分条件与充分必要条件、两个矩阵乘积为复正定矩阵的充分必要条件、两个矩阵的Hadamard乘积是复正定矩阵的条件及其相关性质4个方面研究了复正定矩阵的性质,共给出了有关的20个命题,并证明了其中部分结论,而另一部分结论的证明容易在相关文献中查到.This paper attempts to study the following properties of the complex positive definite matrix including the operational property of the complex positive definite matrix as the sufficient and necessary c conditions of the complex positive definite matrix, the products of two matrixes as the sufficient and necessary conditions of the sufficient and necessary conditions of the complex positive definite matrix and Hadamard products of two matrixes as the conditions and the relative properties of the complex positive definite matrix. The author assigns 20 relative proposition in all and demonstrates some of the conclusion. It is easy to consult the demonstrations of the other conclusions in the relative documents.

关 键 词：复正定矩阵 充分必要条件 HADAMARD乘积 复矩阵 矩阵乘积 证明 充分条件 结论 运算性质 命题 

分 类 号：O151.21[理学—数学] G633[理学—基础数学]