The rotation of eigenspaces of perturbed matrix pairs II
Luka Grubišić, Ninoslav Truhar, Suzana Miodragović · Linear and Multilinear Algebra · 2013
This paper studies the perturbation theory for spectral projections of Hermitian matrix pairs , where is a non-singular Hermitian matrix which can be factorized as , and is positive definite. The class of allowed perturbations is so restricted that the corresponding perturbed pair must have the form , and is positive definite. The main contribution of the paper is a theorem which generalizes the main result from the first part of the paper to this more general setting. Our estimate, in its most general form, depends on a uniform norm bound on a set of all -unitary matrices which diagonalize . The second main contribution is a new sharp uniform estimate of a norm of all -unitary matrices which diagonalize such that is a quasi-definite matrix. The case of a quasi-definite pair is therefore the case where our bounds are most competitive. We present numerical experiments to corroborate the theory.