Angles Between Subspaces and Application to Perturbation Theory

Abstract

<p> It is known that when two subspaces of a Hilbert space are in some sense close to each other, then there exists a unitary operator which is called the direct rotation. This operator maps one of the subspaces onto the other while being as close to identity as possible. In this thesis we study such a pair of subspaces, and the application of the angles between them to the invariant subspace perturbation theory We also develop an efficient algorithm for computing the direct rotation for pairs of subspaces of relatively small dimension. </p>