Recall that the scalar product
of two four- vectors is 
:
so
where
are the components of the metric tensor .
We can think of the metric tensor as a map which
takes two four- vectors 
and 
into the reals:
.
The map is linear in the arguments, in the sense that
We can generalize this by defining a tensor of type 0/N as a map which
takes N four- vectors into the reals which is linear in all its arguments,
for example the metric tensor is a type 0/2 tensor.