An optimal perturbation bound

摘要

Cai and Zhang establish separate perturbation bounds for sin Theta distances with spectral and Frobenius norms (Cai T, Zhang A. Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60-89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well.