Matrices With Gaussian Noise: Optimal Estimates for Singular Subspace Perturbation
Matrices With Gaussian Noise: Optimal Estimates for Singular Subspace Perturbation
The Davis–Kahan–Wedin <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sin \Theta $ </tex-math></inline-formula> theorem describes how the singular subspaces of a matrix change when subjected to a small perturbation. This classic result is sharp in the worst case scenario. In this paper, we prove a stochastic version of the Davis–Kahan–Wedin <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> …