  Low rank matrix recovery problems, including matrix completion and matrix
sensing, appear in a broad range of applications. In this work we present GNMR
-- an extremely simple iterative algorithm for low rank matrix recovery, based
on a Gauss-Newton linearization. On the theoretical front, we derive recovery
guarantees for GNMR in both the matrix sensing and matrix completion settings.
Some of these results improve upon the best currently known for other methods.
A key property of GNMR is that it implicitly keeps the factor matrices
approximately balanced throughout its iterations. On the empirical front, we
show that for matrix completion with uniform sampling, GNMR performs better
than several popular methods, especially when given very few observations close
to the information limit.
