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Pré-Publication, Document De Travail Année : 2018

Eigenvectors of a matrix under random perturbation

Florent Benaych-Georges
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Nathanaël Enriquez
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Alkéos Michaïl
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Résumé

In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent, centered, with a variance profile. This is done through a perturbative expansion of spectral measures associated to the state defined by a given vector.

Dates et versions

hal-01705890 , version 1 (10-02-2018)

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Florent Benaych-Georges, Nathanaël Enriquez, Alkéos Michaïl. Eigenvectors of a matrix under random perturbation. 2018. ⟨hal-01705890⟩
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