  The simple reflection of a light beam of finite transverse extent from a
homogenous interface gives rise to a surprisingly large number of subtle shifts
and deflections which can be seen as diffractive corrections to the laws of
geometrical optics [Goos-H\"anchen shifts] and manifestations of optical
spin-orbit coupling [Imbert-Fedorov shifts], related to the spin Hall effect of
light. We develop a unified linear algebra approach to dielectric reflection
which allows for a simple calculation of all of these effects and lends itself
to an interpretation of beam shifts as weak values in a classical analogue to a
quantum weak measurement. We present a systematic study of the shifts for the
whole beam and its polarization components, finding symmetries between input
and output polarizations and predicting the existence of material independent
shifts.
