Chap 12. And then there are tensors.

We have vectors that have components in the form

that are scalars for basis of the form

Then we have simple q-vectors that have components

that are scalars for basis of the form

Then we have covectors, or 1-forms

with basis

and simple p-forms

with basis

Now we get these

tensor things, which we are only given the component form, something like

Am I correct in assuming the basis of such an animal is something like

?

Or would it be something like

?

Or some other permutation of vectors and 1-forms?