Posted by haifeng on 2021-09-06 08:04:18 last update 2021-09-06 08:04:18 | Answers (0) | 收藏
设 $A,B$ 为半正定(positive semidefinite)矩阵, 根据 Jensen 不等式, 有
\[ \Bigl[\mathrm{tr}(A^s+B^s)\Bigr]^{\frac{1}{s}}\leqslant \Bigl[\mathrm{tr}(A^r+B^r)\Bigr]^{\frac{1}{r}},\quad\forall\ s > r > 0. \]
