On the Structure of the Eigenvectors of Large Hermitian Toeplitz Band Matrices
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The paper is devoted to the asymptotic behavior of the eigenvectors of banded Hermitian Toeplitz matrices as the dimension of the matrices increases to infinity. The main result, which is based on certain assumptions, describes the structure of the eigenvectors in terms of the Laurent polynomial that generates the matrices up to an error term that decays exponentially fast. This result is applicable to both extreme and inner eigenvectors.
Mathematics Subject Classification (2000)Primary 47B35 Secondary 15A18 41A25 65F15
KeywordsToeplitz matrix eigenvector asymptotic expansions
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