复正定矩阵行列式的广义Minkowski不等式

The Generalized Minkowski Inequalities of Determinant for Complex Positive Definite Matrix

给出了n阶复矩阵的广义Minkowski行列式的两个不等式 :|det(A +B) |α≥ 2 -sα2 (|detA|α+|detB|α) ,其中A是n阶复半正定矩阵 ,B是n阶正定Hermite矩阵 ,α≥ 1n,S是B-1A的复特征值的个数 ;|det(A +B) |α≥ (|detA|α+|detB|α) ,其中A和B是n阶复半正定矩阵 ,且它们的特征值全为实数 ,r([A ,B])≤ 1,α≥ 1n,改进和推广了已有的结果 .

Two generalized Minkowski inequalites of determinant for complex matrices are given:｜det( A+B)｜ α≥2 -sα 2 (｜det A｜ α +｜det B｜ α ), Where A be a nxn complex positive definite matrix, B be a nxn positive definite Hermite matrix, α≥1n, s is the number of complex eigenvalues of B -1 A; ｜det( A+B)｜ α ≥｜det A｜ α +｜det B｜ α , Where A and B are nxn complex positive definite matrices, and the eigenvalues are real, r([A,B])≤1,α≥1n .