On the asymptotic behavior of the eigenvectors of large banded Toeplitz matrices
Albrecht Böttcher, Sergei M. Grudsky, Enrique Ramírez de Arellano · Mathematische Nachrichten · 2005
Abstract Let λ be an eigenvalue of an infinite Toeplitz band matrix A and let λn be an eigenvalue of the n ×n truncation An of A . Suppose λn converges to λ as n → ∞. We show that generically the eigenspaces for λn are onedimensional and contain a vector xn whose first component is 1 if only n is large enough, and we prove that xn converges to an eigenvector x 0 of A that is independent of the particular choice of the λn . 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)