  Wigner's classical theorem on symmetry transformations plays a fundamental
role in quantum mechanics. It can be formulated, for example, in the following
way: Every bijective transformation on the set L of all 1-dimensional subspaces
of a Hilbert space H which preserves the angle between the elements of L is
induced by either a unitary or an antiunitary operator on H. The aim of this
paper is to extend Wigner's result from the 1-dimensional case to the case of
n-dimensional subspaces of H with n fixed.
