正定复矩阵行列式的两个不等式

Two inequalities of complex positive definite matrix determinant

给出正定复矩阵的两个不等式 :设A是n阶正定复矩阵 ,B是n阶正定Hermite矩阵 ,则A +B s≥A s+B s;设A、B是n阶正定复矩阵 ,且它们的特征值都是实数 ,又r([A ,B])≤ 1,而sn≥ 1,则A +B s≥A s+B s。将Minkowski不等式推广到正定复矩阵上去。

This paper provides two inequalities of complex positive definite matrix. If A is a complex positive definite matrix of n×n, B is a positive definite Hermite matrix of n×n, then A+B s≥A s+B s;If A and B both are complex positive definite matrix of n×n, their egenvalues both are real, r()≤1,sn≥1,thenA+B s≥A s+B s The Minkowski inequality is extended to the domain of complex positive definite matrix.