We have the following maximization problem
$\max_X \text{Real}(\text{Tr} (AX)),~~~\text{s.t.}~\text{Tr}(X) \le P, ~~X \geq 0$
And $A$ and $X$ are complex square matrices of the same size. Is the solution to the above problem $X=P\dfrac{A^H}{||A||_F}$?