RELATIVE PERTURBATION BOUND FOR INVARIANT SUBSPACES OF HERMITIAN MATRIX
Ninoslav Truhar, Ivan Slapničar · University of Zagreb University Computing Centre (SRCE) · 2000
We give bound for the perturbations of invariant subspaces of nonsingular Hermitian matrix H under relative additive perturbations of H. Such perturbations include the case when the elements of H are known up to some relative tolerance. Our bound is, in appropriate cases, sharper than the classical bounds, and it generalizes some of the recent relative perturbation results. Mathematics subject classification (1991): 15A42, 65F35, 15A60. Key words and phrases: Hermitian matrix, invariant subspace, spectral projection, perturbation bound. 1 Introduction and preliminaries We consider the Hermitian eigenvalue problem H = QQ = n X i=1 i q i q i ; where H is a non-singular Hermitian matrix of order n, = diag( i ) is a diagonal matrix whose diagonal elements are the eigenvalues of H, and Q = [ q 1 q 2 \\Delta \\Delta \\Delta q n ] is unitary matrix whose i-th column is the eigenvector which corresponds to i . We denote the set of all eigenvalues of H by oe(H) = f 1 ; \\Delta \\D...