一个矩阵不等式的推广

EXTENSION OF THE INEQUALITY FOR THE MATRICES

在［１］和［２］中分别在Ａ，Ｂ是正定时称矩阵和正定爱密特矩阵的条件下给出了矩阵不等式｜λＡ＋（１－λ）Ｂ｜≥｜Ａ｜λ｜Ｂ｜１－λ，０≤λ≤１。本文推广了这一工作使上不等式适用于更广泛一类矩阵，而将［１］，［２］的结果作为其推论。

Let A and B be positive defint matrices [1] or positive definitive definitive Hermitiian[2], then |λA+(1-λ)B|≥|A|λ|B|1-λ, 0≤λ≤1.In this paper we generalize the inequality above to another class of matrices. Our results imply the results in [1] and [2] (m=2).