正定矩阵乘积的正定性  

Positive Definiteness of Products of Positive Definite Matrices

作　　者：杨敏 张孝金 YANG Min;ZHANG Xiaojin(School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,China)

机构地区：[1]江苏师范大学数学与统计学院,江苏徐州221116

出　　处：《高等数学研究》2023年第1期4-6,共3页Studies in College Mathematics

基　　金：国家自然科学基金面上项目(12171207);江苏师范大学科研启动基金。

摘　　要：本文给出了两个、三个正定矩阵乘积是正定矩阵的充要条件,研究了n个正定矩阵乘积是正定矩阵的充分条件.并给出了n个正定矩阵乘积正定的必要条件.In this paper, we present necessary and sufficient conditions for the product of two or three positive definite matrices being positive definite, and give a sufficient condition for the product of n positive definite matrices being positive definite.Moreover, the necessary conditions of the products of n positive definite matrices being positive definite are also given.

关 键 词：正定矩阵 实对称矩阵 矩阵乘积 

分 类 号：O154.2[理学—数学]