Given a matrix, the singular values of that matrix are uniquely determined.If that matrix is square, and the singular values are distinct, the left and right singular vectors are uniquely determined up to a sign.These are suppose to be corollaries of the relation between SVD's and eigenvalues decomposition, i.e. that if ????=????Σ????′A=UΣV′, then ????′????=????Σ2????′A′A=VΣ2V′.