Before revision:  Intriguingly, while the singular subspaces are known to be extremely sensitive to additive noises, the proposed error bound holds universally for perturbations with arbitrary magnitude  .
After revision:  Intriguingly, while the singular subspaces are known to be extremely sensitive to additive noises, the proposed error bound holds universally for perturbations with arbitrary magnitude . Finally, we demonstrate an application of our results to the analysis of the mean squared error associated with the TSVD-based matrix denoising solution .