Perturbation theory for Hermitian matrix-functions based on vector-fields

Abstract: We consider "spectral" matrix-functions for Hermitian matrices, where the novelty is that the function applied to the spectrum is allowed to be a vector-field rather than a scalar function (a.k.a isotropic matrix functions). We prove first order approximation formulas, generalizing the classical Daleskii-Krein theorem, as well as Lipschitz estimates.