关于正定矩阵的Szász不等式和Hadamard不等式的注记  

Notes on Szász′s inequality and Hadamard′s inequality of a positive definite matrix

作　　者：刘合国 高睿 徐行忠 廖军 Liu Heguo;Gao Rui;Xu Xingzhong;Liao Jun(School of Mathematics and Statistics,Hubei University,Wuhan 430062,China)

机构地区：[1]湖北大学数学与统计学学院,湖北武汉430062

出　　处：《纯粹数学与应用数学》2021年第2期127-136,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(11771129,11971155,12071117).

摘　　要：在矩阵不等式理论里,Szász不等式和Hadamard不等式是基本的结论.给出Szász不等式的加法形式,证明Hadamard不等式等价于AM-GM不等式,这些定论似乎被矩阵论专家忽视了.从一个侧面揭示了“平均”思想的重要作用.In the theory of matrix inequalities, Szász′s inequality and Hadamard′s inequality are the basic conclusions. In this paper, we give the additive form of Szász′s inequality and prove that Hadamard′s inequality is equivalent to the AM-GM inequality, which seem to be ignored by matrix theory experts. This paper reveals the important role of the idea of average from one aspect.

关 键 词：正定矩阵 Szász不等式 HADAMARD不等式 AM-GM不等式 

分 类 号：O151[理学—数学]