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We consider the non-square matrix sensing problem, under restricted isometryproperty (RIP) assumptions. We focus on the non-convex formulation, where anyrank-$r$ matrix $X \in \mathbb{R}^{m \times n}$ is represented as $UV^\top$,where $U \in \mathbb{R}^{m \times r}$ and $V \in \mathbb{R}^{n \times r}$. Inthis paper, we complement recent findings on the non-convex geometry of theanalogous PSD setting [5], and show that matrix factorization does notintroduce any spurious local minima, under RIP.

Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach