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arXiv · 0901.3436

Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

Hui Dai·Zachary Geary·Leo P. Kadanoff
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Abstract

A Toeplitz matrix is one in which the matrix elements are constant along diagonals. The Fisher-Hartwig matrices are much-studied singular matrices in the Toeplitz family. The matrices are defined for all orders, $N$. They are parametrized by two constants, $α$ and $β$. Their spectrum of eigenvalues has a simple asymptotic form in the limit as $N$ goes to infinity. Here we study the structure of their eigenvalues and eigenvectors in this limiting case. We specialize to the case $0<α<|β|<1$, where the behavior is particularly simple.

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Hui Dai, Zachary Geary, Leo P. Kadanoff. 2009-04-18. Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices. https://doi.org/10.1088/1742-5468%2F2009%2F05%2Fp05012

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