Orthogonal matrices having elements depending on certain random vectors provide a useful tool in various distribution problems in multivariate analysis. The method is applied to the derivation of the distributions of Hotelling's $T^2$ and Wilks' generalized variance, the Bartlett decomposition, and the Wishart distribution.
"Random Orthogonal Transformations and their use in Some Classical Distribution Problems in Multivariate Analysis." Ann. Math. Statist. 28 (2) 415 - 423, June, 1957. https://doi.org/10.1214/aoms/1177706969