Before revision:  We derive the perturbation bound for the singular value thresholding operator applied to full-rank matrices. We derive an improved \ell_{2\rightarrow \infty bound on singular vectors, which matches the best-known results for eigenvectors derived under more restricted conditions.
After revision:  We derive the perturbation bound for the singular value thresholding operator \rightarrow \infty bound on singular vectors, which matches the best-known results for eigenvectors derived under more restricted conditions.