ABSTRACT
The basis {dxi} of 1-forms is quite natural and is called a coordinate basis. However, in the presence of an inner product g on
∧1, it is often preferable to work instead with an orthonormal basis. So let’s start over
and work with an arbitrary (for now) basis. Suppose {σi} is a basis of ∧1. Then a basis for
∧p is
{σI} = {σi1 ∧ ... ∧ σip}, (14.1)
where the index set I = {i1, ..., ip} satisfies 1 ≤ i1 < ... < ip ≤ n, and where we are of course assuming p ≤ n.
