Abstract: In this paper, we generalize the Wielandt-Hoffman theorem, one of the important theorems on real symmetric matrix theory, to the corresponding-theorem on Hermitian matrices. We improve the estimation of the eigenvalues of AB for A>0, B>0, by this theorem, and from this theorem we give the matrix analogue of arithmetic mean-geometric mean, Holder, and Minkowski inequalities.

Key words: Hermitian matrice, matrix trace, eigenvalue, inequality

摘要： 本文首先推广实对称矩阵理论中的Wielandt-Hoffman定理到复数矩阵上。然后,我们利用这个推广结果给出了两正定厄米特矩阵乘积的特征值的新估计,它改进了文[4]中结果。最后,我们还给出了算术平均-几何平均不等式,Hlder不等式和Minkowski不等式的矩阵迹类似。

关键词: 厄米特矩阵, 矩阵迹, 特征值, 不等式