关于Hermite矩阵迹的不等式

On the inequalities for trace of Hermitian matrices

获得不等式 :( 1 ) tr ( AB) m≤ tr ( Am Bm) ;( 2 ) tr ( A B) m≤ tr ( Am Bm)。其中 A、B为 Hermite矩阵 ,m为正偶数。

For Hermitian matrices A and B,the following inequalities are proved: (1)tr(AB) m ≤tr(AmBm);(2)tr(AB)m≤tr(A m B m),where m is a positive,even number.