Asymptotic procedures are given for testing certain hypotheses concerning eigenvectors and for constructing confidence regions for eigenvectors. These asymptotic procedures are derived under fairly general conditions on the estimates of the matrix whose eigenvectors are of interest. Applications of the general results to principal components analysis and canonical variate analysis are given.
"Asymptotic Inference for Eigenvectors." Ann. Statist. 9 (4) 725 - 736, July, 1981. https://doi.org/10.1214/aos/1176345514