Perturbation of linear forms of singular vectors under Gaussian noise

Vladimir Koltchinskii, Dong Xia

Let $A\in {\mathbb{R}}^{m\times n}$ be a matrix of rank $r$ with singular value decomposition (SVD) $A={\sum }_{k=1}^r{\sigma }_k(u_k\otimes v_k),$ where $\{{\sigma }_k,k=1,\dots ,r\}$ are singular va…