半正定矩阵乘积的特征值估计

ESTIMATION OF THE EIGENVALUES OF AB FOR A≥O, B≥O

本文给出了两个半正定Hermite矩阵乘积的特征值估计,它改述了[2][4]中的 果。

This paper gives the estimation of the eigenvalues of AB for A≥0,B≥0. It improves the conclusion in [1][2]. Theorem Suppose A, B are both Semi-positive definite Hermite matrices. u1, un are the least, the largest eigenvalues of A respectively, v1, vn are the least, the largest eigenvalues of B respectively, if λ1, λ2, …, λn are the eigenvalues of AB, then