Perturbation analysis of the eigenvector matrix and singular vector matrices

Abstract

Let A be an n×n Hermitian matrix and A = UΛUH be its spectral decomposition, where U is a unitary matrix of order n and Λ is a diagonal matrix. In this note we present the perturbation bound and condition number of the eigenvector matrix U of A with distinct eigenvalues. A perturbation bound of singular vector matrices is also given for a real n×n or (n+1)×n matrix. The results are illustrated by numerical examples.