Fan,　Wang,　and　Zhong　estimate　the　difference　between　the　singular　vectors　of　a　matrix　and　those　of　a　perturbed　matrix　in　terms　of　the　maximum　norm.　Their　estimations　are　used　effectively　to　establish　the　asymptotic　properties　of　robust　covariance　estimators　(see　Journal　ofMachine　Learning　Research,　2018;18:1-42).　In　this　paper,　we　give　the　corresponding　lower　bound　estimates,　which　show　Fan-Wang-Zhong＇s　estimations　optimal.