Speaker
Description
In this talk, we will discuss the perturbation of a Hermitian matrix pair (H, M), where H is non-singular and M is a positive definite matrix. The corresponding perturbed pair (\widetilde{H}, \widetilde{M}) = (H + \delta H, M + \delta M) is assumed to satisfy the conditions that \widetilde{H} remains non-singular and \widetilde{M} remains positive definite. We derive an upper bound for the tangent of the angles between the eigenspaces of the perturbed and unperturbed pairs. The rotation of the eigenspaces due to perturbation is measured in a matrix-dependent scalar product.
We will demonstrate that the absolute and relative \tan \Theta bounds for the standard eigenvalue problem are special cases of our newly derived bounds. Additionally, we will show how this bound can be applied to stable gyroscopic systems.
