Formes normales de perturbations de matrices : étude et calcul exact

Abstract : This thesis deals with rational normal forms of matrix perturbations and the eigenvalue perturbation problem : the asymptotic behavior of perturbed eigenvalues only depends on a few monomials of the characteristic polynomial and the goal is thus to be able to "recover" these monomials directly from the initial matrix (quasi-generic perturbations) or at least from a similar matrix perturbation (reduced form). Following Moser and Lidskii, we define two reduced forms that are associated with two different families of quasi-generic matrix perturbations. We also extend Lidskii's perturbation theorem in order to give a third reduced form and to provide a complete solution to the problem. Additionally, a Newton diagram interpretation is detailed for each of these results and some Maple functionalities for handling matrix perturbations are described.
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Claude-Pierre Jeannerod. Formes normales de perturbations de matrices : étude et calcul exact. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 2000. Français. ⟨tel-00006747⟩

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