Recall that a vector can be regarded as a 1/0 tensor [ i.e. a map of one- forms into the reals ]. Therefore the outer product of two vectors defines a 2/0 tensor, i.e. it is a linear map from two one- forms to the reals:
It follows that the most general 2/0 tensor is a linear sum of such outer products:
where
Under a Lorentz transformation, the components of f are:
As before we can separate f into symmetric and anti- symmetric parts:
and
