Some one can help me with this problem?
I have two real positive-semidefinite matrices $P$ and $Z$, $P \succeq 0$, $Z \succeq 0$, and they are both symmetric ($P^T = P$ and $Z^T = Z$). Also trace$ (P\cdot Z) = 0$. Does that mean $P \cdot Z = 0$ ? Assume they are both $n \times n$ square matrices. Thanks！