The Rotation of Eigenspaces of Perturbed Matrix Pairs
Provides sharper theoretical bounds for spectral subspace rotation in parameter-dependent eigenvalue problems, relevant to numerical linear algebra and perturbation analysis.
The paper revisits relative perturbation theory for invariant subspaces of positive definite matrix pairs, deriving new estimates that yield sharp bounds on the rotation of spectral subspaces as functions of a parameter indexing the family of matrix pairs.
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates are a natural way to obtain sharp --- as functions of the parameter indexing the family of matrix pairs --- estimates for the rotation of spectral subspaces.