Suppose we have matrices $Q, K, V \in \mathbb{R}^{n \times n}$ and $P = QK^\top$ is of rank $k$. We want to prove that there exist two matrices $C, D \in \mathbb{R}^{k \times n}$ such that $PV = Q(CK)^\top DV$.
I think singular value decomposition can help, but after writing down the SVD of $P$ I don't know how to proceed.
Anyone share some hint?