On Transformations and Perturbations of Orthogonal r-Frames

Abstract

A decomposition of Cn into a finite direct sum of orthogonal subspaces can be conveniently represented by its orthogonal projector frame, which is the collection of the corresponding orthogonal projectors. Two such decompositions whose frames are close, are known to be linearly homeomorphic and homotopic. In a recent work we compared the resulting geodesic arcs with naturally arising paths, resulting from interpolating the balanced transformation and found them cubically close. In this work we describe an efficient algorithm to compute the balanced transformation.