Chandler-Wilde, Chonchaiya and Lindner conjectured that the set ofeigenvalues of finite tridiagonal sign matrices ($\pm 1$ on the first sub- andsuperdiagonal, $0$ everywhere else) is dense in the set of spectra of periodictridiagonal sign operators on $\ell^2(\mathbb{Z})$. We give a simple proof ofthis conjecture. As a consequence we get that the set of eigenvalues oftridiagonal sign matrices is dense in the unit disk. In fact, a recent paperfurther improves this result, showing that this set of eigenvalues is dense inan even larger set.
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