Projections on unstructured subspaces

Abstract

Orthogonal projection on vector subspaces arises in many applied fields. The common assumption about the orthogonal complementary subspace is that it is spanned by white noise components. We generalize a previous perturbation analysis of projection operators to that with a noise field with an arbitrarily structured covariance matrix. The resulting expressions are insightful, and their algebraic power is very useful for applications.