An optimal perturbation bound

Abstract

Cai and Zhang establish separate perturbation bounds for sinnormalΘ 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.