Matrices perturbed by random noise: The accuracy of low-rank approximation

Phuc Tran, Van Vu

Let $A$ be an $m\times n$ matrix with rank $r$ and singular value decomposition $A={\sum }_{i=1}^r{\sigma }_i{u}_i{v}_i^{\top },$ where the ${\sigma }_i$ are its singular values, ordered decreasingl…