Eigenvectors of a matrix under random perturbation

Florent Benaych-Georges; Nathanaël Enriquez; Alkéos Michaïl

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arXiv · 1801.10512

Eigenvectors of a matrix under random perturbation

Florent Benaych-Georges·Nathanaël Enriquez·Alkéos Michaïl

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Abstract

In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix of 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.

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BibTeX RIS

Florent Benaych-Georges, Nathanaël Enriquez, Alkéos Michaïl. 2018-01-31. Eigenvectors of a matrix under random perturbation. https://arxiv.org/abs/1801.10512

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