A relative perturbation bound for positive definite matrices
The author gives an asymptotically sharp bound on the angles between perturbed and unperturbed eigenvectors of a symmetrically perturbed symmetric positive definite matrix. The estimate implies also a bound on the perturbation of the eigenvectors. The proof is surpassingly simple. (There is an unpleasant misprint in the statement of Theorem 1 where ``+'' in equation (2) should be replaced by ``-'').
scientific article; zbMATH DE number 1109506