  Every sufficiently big matrix with small spectral norm has a nearby low-rank
matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM
J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the
estimate of the distance for matrices with incoherent column and row spaces. In
numerical experiments with several classes of matrices we study how well the
theoretical upper bound describes the approximation errors achieved with the
method of alternating projections.
