实正定和反对称矩阵的若干不等式

Several inequalities of real positive definite and skew symmetric matrices

主要研究了实定矩阵的一些相似不变量.关于正定矩阵的迹给出了一组交换条件下的不等式,行列式得到了一个有用的结果,一些著名的矩阵不等式可由其导出.此外还给出了反对称矩阵的相关不等式.

This paper concentrates on some properties of positive definite matrices＇ similar invarirants. For their traces, we give a group of inequalities under the commutative condition. For their determinants, we have obtained a useful result by which some famous inequalities can be deduced, Moreover, some relavant results for skew symmetric matrices are also shown in this paper.