Let A be an m × n-matrix which is slightly perturbed. In this paper we will derive an estimate of how much the invariant subspaces of AUA and AA H will then be affected. These bounds have the sin 0 theorem for Hermitian linear operators in Davis and Kahan [1] as a special case. They are applicable to computational solution of overdetermined systems of linear equations and especially cover the rank deficient case when the matrix is replaced by one of lower rank.
A perturbation theory for pseudo-inverses is developed. The theory is based on a useful decomposition (theorem 2.1) of B+ -A + where B and A are m x n matrices.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.