We mention a dichotomy drawn from exterior algebra. A bivector that can be written as F = v ∧ w, where v, w are linearly independent, is called simple. Any nonzero bivector over a 4-dimensional vector space either is simple, or can be written as F = v ∧ w + x ∧ y, where v, w, x, and y are linearly independent; the two cases are mutually exclusive. Stated like this, the dichotomy makes no reference to the metric η, only to exterior algebra. But it is easily seen that the associated skew-symmetric linear operator F b has rank 2 in the former case and rank 4 in the latter case.