Haynsworth矩阵不等式的推广

Generalization of Haynsworth Matrix Inequality

首先指出关于正定Hermitian矩阵的Haynsworth矩阵不等式对半正定Hermitian矩阵是不成立的;然后给出一个无约束条件的Haynsworth矩阵不等式的在半正定Hermitian矩阵的推广形式。

First, we point out that the Haynsworth matrix inequality on positive definite Hermitian matrix does not work for generalized positive semidefinite matrix. Second, an unconditional Haynsworth matrix inequality for positive semidefinite Hermitian matrix is presented.