和与积相等的Hermitian矩阵对的惯性及应用  

Inertia of Hermitian matrix pairs whose sum is equal to its product and its applications

作　　者：林志兴 杨忠鹏 陈梅香 陈智雄 LIN Zhixing;YANG Zhongpeng;CHEN Meixiang;CHEN Zhixiong(School of Mathematics and Finance, Putian University, Putian, Fujian 351100, China)

机构地区：[1]莆田学院数学与金融学院,福建莆田351100

出　　处：《福州大学学报（自然科学版）》2018年第1期27-31,共5页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61373140);福建省自然科学基金资助项目(2017J01565);福建省高校杰出青年科研人才培育计划(2016);福建省教育厅中青年教师教育科研资助项目(JAT170499);莆田学院教改资助项目(JG201630);莆田学院育苗基金资助项目(2016110)

摘　　要：针对文献[5]在和与积相等的正定矩阵对的Kantorovich型矩阵不等式证明中所使用的等式是不成立的情况,提出沟通Hermitian矩阵的特征值与惯性关系的方法,得到了和与积相等的Hermitian矩阵对的惯性一般表达式.不仅证明了文献[5]的矩阵不等式是正确的,而且给出使这类正定(或半正定)矩阵对的通常乘积更精细的矩阵不等式.As the equality used in the proof of Kantorovich＇ inequality in for positive detinite Herrm tian matrix pairs, whose sum is equal to its product, is defective, this paper mediates the relationship between eigenvalue and inertia of Hermitian matrix, and gives us the general expression for Inertia of Hermitian matrix pairs, whose sum is equal to its product. By applications, it not only proves that Kantorovieh＇ inequality is correct, but also shows some more precise matrix inequalities for product of this class of positive definite （semi-definite） Hermitian matrix pairs.

关 键 词：HERMITIAN矩阵 惯性 矩阵方程 秩 

分 类 号：O151.21[理学—数学]