  Nonexpansive mappings play a central role in modern optimization and monotone
operator theory because their fixed points can describe solutions to
optimization or critical point problems. It is known that when the mappings are
sufficiently "nice", then the fixed point set of the composition coincides with
the intersection of the individual fixed point sets. In this paper, we explore
the situation for compositions of linear reflectors. We provide positive
results, upper bounds, and limiting examples. We also discuss classical
reflectors in the Euclidean plane.
