关于矩阵乘积迹的两个不等式

Two Inequalities of Matrices Multiplicative Trace

本文证明了矩阵乘积迹的两个不等式,即定理1和定理2。定理1给出m个方阵乘积迹的上界,这上界是这m个方阵的奇异值的函数。定理2给出m个半正定阵乘积迹的上界,这上界是这m个半正定阵幂迹的函数。

In this paper, the two inequalities of the matrices multiplicative trace are proven, i.e. theorem 1 and theorem 2. In theorem 1, the upper bound of m square matrices multiplicative trace is given, which is the function of the singular values of these m square mat-rice. In theorem 2, the upper bound of m semi-definite matrices multiplicative trace is given, which is the function of these m semid-efinite matrices power trace.