Distributions of projections of uniformly distributed K-frames

A geometrical perspective is introduced that enables unification and generalization of several results regarding the distributions of quantities that arise in connection with an important class of multiple-channel detectors. Standard models on sets of normalized vectors following from joint Gaussian assumptions in this context are relaxed to the geometrically appealing model of uniform distributions on the Stiefel manifold of K-frames in N-dimensional space. In addition to bolstering geometric insight, several prior results are subsumed and strengthened by results obtained under this formulation. Additionally, a generalization of a classical theorem of W. G. Cochran is enabled by this framework.