Black polarization sandwiches are square roots of zero

In the 2 x 2 matrices representing retarders and ideal polarizers, the eigenvectors are orthogonal. An example of the opposite case, where eigenvectors collapse onto one, is matrices M representing crystal plates sandwiched between a crossed polarizer and analyser. For these familiar combinations, M-2 = 0, so black sandwiches can be regarded as square roots of zero. Black sandwiches illustrate physics associated with degeneracies of non-Hermitian matrices.