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

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.