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?