# Reference showing global optimality of local minima for matrix factorization

Consider the following matrix factorization problem: Given an $$n\times m$$ matrix M, find $$n\times r$$ and $$m\times r$$ matrices $$U$$ and $$V$$ such that $$||UV^T - M||_F^2$$ is minimized.

I have heard it many times that all the local minima are global minima for this problem, and that all other stationary points have some direction with negative curvature. I am looking for a reference that rigorously shows this for any asymmetric matrix $$M$$.