Tensors of type 0/2
It is therefore a 0/2 tensor. denotes the outer product. It is the formal notation to show how the 0/2 tensor is formed from two one- forms.
Note that this product is non- commutitative since gives a different result [ Assignment 3 ] i.e.
The most general 0/2 tensor is a linear sum of such outer products. So
where are the components of the map f and we have used linearity.
so we have
with the symmetric and anti- symmetric parts given by