On the largest principal angle between random subspaces

Formulas are derived for the probability density function and the probability distribution function of the largest canonical angle between two p-dirnensional subspaces of R-n chosen from the uniform distribution on the Grassmann manifold (which is the unique distribution invariant by orthogonal transformations of R-n). The formulas involve the gamma function and the hypergeometric function of a matrix argument. (c) 2005 Elsevier Inc. All rights reserved.