Differentiable roots, eigenvalues, and eigenvectors

Abstract

We determine the conditions for the existence of $C^p$-roots of curves of monic complex polynomials as well as for the existence of $C^p$-eigenvalues and $C^p$-eigenvectors of curves of normal complex matrices.

18 pages, some typos corrected, accepted for publication in Israel J. Math

References in corpus (3)

• Perturbation theory for normal operators
• Quasianalytic multiparameter perturbation of polynomials and normal matrices
• Smooth roots of hyperbolic polynomials with definable coefficients

Cited by in corpus (5)

• A new proof of Bronshtein's theorem
• Tracking Particles in Flows near Invariant Manifolds via Balance Functions
• Lifting differentiable curves from orbit spaces
• Re-parameterizing and reducing families of normal operators
• Selections of bounded variation for roots of smooth polynomials