How to solve the following optimization problem which arises in the field of Higher Order SVD?
Let $A \in \mathbb{R}^{m\times n}$, $W \in \mathbb{R}^{m\times l}$.
find $\arg \max _{A}\|A^T W\|_F$ s.t. $A$ columnwise orthogonal.
$\| \cdot \|_{F}$ here represents the Frobenius norm. I know the solution is the matrix containing the left singular values of $W$, but it is not clear to me why.