关于半正定矩阵迹的几何—算术平均不等式

THE GEOMETRIC-ARITHMETRIC-MEAN INEQUALITY FOR POSITIVE SEMIDEFINITE MATRIX TRACES

本文首先证明了关于Hermite矩阵迹的一个不等式,在此基础上,得出了关于半正定矩阵迹的几何-算术平均不等式,特别地,该不等式对实对称半正定阵也是成立的,这就给出了文〔1〕中,R.Bellman所提问题的一个回答。

In this paper, we firstly prove an inequality for Hermite matrix traces, then present an -inequality for positive semidefinite Hermite matrix traces. Particularly it holds for real symmetric positive semidefinite matrix traces, thus giving an answer to an open question proposed by R.Bellman.