Shifted Fourier Matrices and Their Tridiagonal Commutors

Abstract

It is known that, for n ≥ 3, the n×n Fourier matrix F = n−1/2[e2π̊ıμν/n] (0 ≤ μ < n, 0 ≤ ν < n) commutes with a nonscalar tridiagonal matrix T and also with another matrix X that is “almost” tridiagonal. These matrices are important in selecting eigenvectors for the Fourier matrix itself. The purpose of this paper is to generalize those results to matrices… (More)
DOI: 10.1137/S0895479800372754

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