About Hölder condition numbers and the stratification diagram for defective eigenvalues

In this paper, we look at a particular case of application which is Hölder continuous, namely the map from a matrix A to one of its eigenvalues λ, when it is multiple defective. Two asymptotic Hölder condition numbers are considered: one (with respect to the other) is associated with a generalization of the Fréchet (with respect to Gateaux) derivative [A. Harrabi, About Hölder condition numbers of Gateaux and Fréchet type for general nonlinear functions, Manuscript — CERFACS, 1998].