一类矩阵迹不等式的推广

A Extension for the Inequalities of Matrix Trace

利用平均值不等式 ,得到关于矩阵迹的不等式 :如果 A1 ,A2 ,… ,Am 皆为 n阶 Hermite半正定矩阵 ,且乘法两两可交换 ,0 <r≤s,则有tr Ar1 +… + Armms≤tr As1 +… + Asmmr 和 tr Ar1 +… + Armm1r≤tr As1 +… + Asmm1s.

Using inequalities on average, the author gives inequalities of matrix trace: if A 1, A 2,..., A m are positive semidefinite Hermite matrix, and they are each other exchangeable on multiplying, 0<r≤s, then tr A r 1+...+ A r mm s≤tr A s 1+...+ A s mm r and tr A r 1+...+ A r mm 1r ≤tr A s 1+...+ A s mm 1s .