## 每週問題 February 27, 2017

Let $A$ and $B$ be Hermitian matrices. We will write that $A\succ B$ if $A-B$ is positive definite. The inequality $A\succ 0$ means that $A$ is positive definite. Prove that if $A\succ B\succ 0$, then $B^{-1}\succ A^{-1}$.