Abstract
In this paper, we consider the perturbation of a Hermitian matrix pair , where H and M are non-singular and positive definite Hermitian matrices, respectively. A novel upper bound on a tangent of the angles between the eigenspaces of perturbed and unperturbed pairs is derived under a perturbation to the off-diagonal blocks of H. The rotation of the eigenspaces under a perturbation is measured in the matrix-dependent scalar product. We show that a bound for the standard eigenvalue problem is a special case of our new bound and that the obtained bound can be much sharper than the existing bounds.
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