矩阵迹的几个不等式

Some Inequalities about Trace of Matrix

本文推广了实对称矩阵理论中的Ｗｉｅｌａｎｄｔ—Ｈｏｆｆｍａｎ定理到复数矩阵上．利用这个结果给出了两正定厄米特矩阵乘积的特征值的新估计．最后，还给出了算术平均一几何平均不等式，Ｈｏｌｄｅｒ不等式和Ｍｉｎｋｏｗｓｋｉ不等式在矩阵迹上的类似．

First,the Wielandt-Hoffman theorem on real symmetric matrix is extended to complex case.Second,using the extended result,new estimations of trigenvalue for the product of two positive Hermite matrices are given,which imporves the results in reference [4].Finally,some inequalities similar to arithmetic average-geometry average inequality,Hoder inequality and Min.inequality are also given in the case of matrix trace.