Before revision: Singular vector perturbation is an important topic in numerical analysis and statistics. The main goal of this paperis to provide a useful tool to tackle matrix perturbation problems. Explicitly , we establish a useful formula for the sin\Theta angles between the perturbed and the original singular subspaces.
After revision: In this paper , we establish a useful formula for the sin\Theta angles between the perturbed and the original singular subspaces.