Define a manifold M with local coordinates [x, y, z, w].
Example 1.
Define a 3-dimensional subspace of vectors by the span of S and compute a simpler base for this subspace relative to the coordinate basis T for the tangent space of M.
We use the command DGEqual to check that the span of S and W agree.
Example 2.
We use the same vectors S as in Example 1 but reverse the ordering of the vectors in the basis S.
We note that the matrix of coefficients of W with respect to T is in reduced row echelon form.
Example 3.
Find a canonical basis for the space of 2-forms spanned by S3.