  We present a derivation of the transformation between the Q and U Stokes
parameters and the E and B scalar and pseudo-scalar fields. We emphasize the
geometrical properties that such transformation must satisfy. We present the E
and B decomposition of some simple maps and of a model for a supernova remnant.
We discuss the relative amplitudes of the E and B components and argue that for
generic random maps E and B should have roughly the same amplitudes.
