  An area metric is a (0,4)-tensor with certain symmetries on a 4-manifold that
represent a non-dissipative linear electromagnetic medium. A recent result by
Schuller, Witte and Wohlfarth provides a pointwise normal form theorem for such
area metrics. This result is similar to the Jordan normal form theorem for
(1,1)-tensors, and the result shows that any area metric belongs to one of 23
metaclasses with explicit coordinate expressions for each metaclass. In this
paper we restate and prove this result for skewon-free (2,2)-tensors and show
that in general, each metaclasses has three different coordinate
representations, and each of metaclasses I, II, ..., VI, VII need only one
coordinate representation.
