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.

翻译：每个具有小谱范数的足够大矩阵，在最大范数下都存在一个邻近的低秩矩阵（Udell \& Townsend, SIAM J Math Data Sci, 2019）。我们利用Hanson--Wright不等式改进了对列空间与行空间非相干矩阵的距离估计。通过多类矩阵的数值实验，研究了理论上限对交替投影方法所达到近似误差的描述程度。