正定Hermite矩阵迹的不等式的几点注记  

Some Notes on the Inequalities of Hermite Matrix Trace

作　　者：宋园[1] SONG Yuan(Foundation Department, Chuzhou Vocational and Technical College, Chuzhou 239000, China)

机构地区：[1]滁州职业技术学院基础部

出　　处：《安庆师范大学学报（自然科学版）》2019年第2期40-41,51,共3页Journal of Anqing Normal University(Natural Science Edition)

基　　金：2018安徽省教育厅高校自然科学基金项目(KJ2018A0839);2016滁州职业技术学院院级质量工程(zlgc2016059,zlgc2016013)

摘　　要：文献[1]中给出了有关正定Hermite矩阵迹的不等式的几个定理,本文通过分析并结合例子说明定理1的证明过程存在问题,进一步通过反例说明定理1是不成立的,同时指出文献中其他几个定理也存在同样的问题。针对证明过程出现的问题,给出矩阵迹的不等式证明中的几点注记。In reference[1], several theorems about inequality of positive definite Hermet matrix trace are given. In this paper, some problems are found through analysis of the proof process, and the problems in the proof process of Theorem 1 are illustrated by combining examples. Further through counterexamples to show that Theorem 1 is not valid. At the same time, it is pointed out that other theorems in the literature also have the same problem. Some notes in the inequality proof of matrix trace are given for the problem of proof process.

关 键 词：不等式 正定HERMITE矩阵 迹 

分 类 号：O151.21[理学—数学]