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On the asymptotic behavior of the eigenvectors of large banded Toeplitz matrices

✍ Scribed by A. Böttcher; S. Grudsky; E. Ramírez de Arellano

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
141 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let λ be an eigenvalue of an infinite Toeplitz band matrix A and let λ~n~ be an eigenvalue of the n ×n truncation A~n~ of A . Suppose λ~n~ converges to λ as n → ∞. We show that generically the eigenspaces for λ~n~ are onedimensional and contain a vector x~n~ whose first component is 1 if only n is large enough, and we prove that x~n~ converges to an eigenvector x ~0~ of A that is independent of the particular choice of the λ~n~ . The eigenspace of A corresponding to λ is spanned by x ~0~ and a finite number of shifts of x ~0~. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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