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arXiv · 1809.09480

Perturbation theory for the spectral decomposition of Hermitian matrices

Marcus Carlsson
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Abstract

Let A and E be Hermitian self-adjoint matrices, where A is fixed and E a small perturbation. We study how the eigenvalues and eigenvectors of A+E depend on E, with the aim of obtaining first order formulas (and when possible also second order) that are explicitly computable in terms of the spectral decomposition of A and the entries in E. In particular we provide explicit Frechet type differentiability results. The findings can be seen as an extension of the Rayleigh-Schr\"odinger coefficients for analytic expansions of one-dimensional perturbations.

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Marcus Carlsson. 2018-09-24. Perturbation theory for the spectral decomposition of Hermitian matrices. https://arxiv.org/abs/1809.09480

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