Answer

问题及解答

线性代数中关于矩阵迹(trace)的不等式

Posted by haifeng on 2021-09-06 08:04:18 last update 2021-09-06 08:04:18 | Edit | Answers (0)

设 $A,B$ 为半正定(positive semidefinite)矩阵, 根据 Jensen 不等式, 有

\[
\Bigl[\mathrm{tr}(A^s+B^s)\Bigr]^{\frac{1}{s}}\leqslant \Bigl[\mathrm{tr}(A^r+B^r)\Bigr]^{\frac{1}{r}},\quad\forall\ s > r > 0.
\]