Let $A\in R^{m\times m}$. Consider the following problem:
$$ \begin{align} \max \,& \langle A, X\rangle\\ \text{s.t.}\,&X'X=I_m\\ &X\in R^{m\times m} \end{align} $$ where $\langle X, Y\rangle =\text{trace}(X'Y)$. This is not a convex problem. Is there an analytical solution for it, or an algorithm?