A pure contravariant tensor of order (p,0) (the 0 shows that a vector space

involved) has the form:

where

is the dual space of

.

I'm having a lot of trouble trying to think of an example! I figure the easiest example is to take a vector space

and any

matrix. These types of matrices will be in the dual space and they will represent a linear map.

To map a linear map to a scalar without using any vectors in

, I figure the easiest way is to just take the determinant of the matrix.

I think this example is okay, but I wondered if there was a better one I could use.

Anyway, my question is: Can anyone think of any other good examples of a pure contravariant tensor?