  Singular Mueller matrices play an important role in polarization algebra and
have peculiar properties that stem from the fact that either the medium
exhibits maximum diattenuation and/or polarizance, or because its associated
canonical depolarizer has the property of fully randomizing, the circular
component (at least) of the states of polarization of light incident on it. The
formal reasons for which the Mueller matrix M of a given medium is singular are
systematically investigated, analyzed and interpreted in the framework of the
serial decompositions and the characteristic ellipsoids of M. The analysis
allows for a general classification and geometric representation of singular
Mueller matrices, of potential usefulness to experimentalists dealing with such
media.
