I want to solve the following maximization problem in $\mathbf{X}\in {\mathbb{R}}^{{m} \times {n}}$
\begin{eqnarray} \begin{split} \quad\max_\mathbf{X} \frac{\mathbf{Tr}(\mathbf{X}^\top \mathbf{Q} \mathbf{X})}{\mathbf{Tr}((\mathbf{X-A})^\top \mathbf{P} (\mathbf{X-A}))} \end{split} \end{eqnarray}
where $\mathbf{A}\in {\mathbb{R}}^{{m} \times {n}}$, $\mathbf{P}\in {\mathbb{R}}^{{m} \times {m}}$ and $\mathbf{Q}\in {\mathbb{R}}^{{m} \times {m}}$ and $\mathbf{P}$, $\mathbf{Q}$ are positive definite matrix.
It is well known that if $\mathbf{A}=\mathbf{O}$, it is easily solved by eigenvalue problem. However, I am not sure how to solve such a problem.