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