Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem

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We extend the perturbation theory of Vishik, Ljusternik and Lidskii for eigenvalues of matrices, using methods of min-plus algebra. We show that the asymptotics of the eigenvalues of a perturbed matrix is governed by certain discrete optimisation problems, from which we derive new perturbation formulae, extending the classical ones and solving cases which where singular in previous approaches. Our results include general weak majorisation inequalities, relating leading exponents of eigenvalues of perturbed matrices and min-plus analogues of eigenvalues.
38 pages, 7 postscript figures, LaTeX2e v1, 5 Feb 04. v2, 20 Jan 05: final example added, more informative title and introduction. v3, 14 Feb 06: references added

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Spectral Theory, 47A55;47A75;05C50;12K10

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http://salesiana.dossiersoluciones.com/handle/123456789/99951

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0402090
 http://arxiv.org/abs/math/0402090

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arXiv