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.