Perturbation analysis of the canonical correlations of matrix pairs

Abstract

AbstractWe present a perturbation analysis of the canonical correlations of matrix pairs. Absolute perturbation bounds for normwise as well as componentwise perturbations are derived. We demonstrate by way of examples that small relative perturbation of a matrix pair does not necessarily imply small relative perturbation in its canonical correlations, and we identify a class of matrix pairs for which good relative perturbation bounds can be derived under certain conditions