Covectors

A covector is a linear map from a vector space to a field of scalars.

• let be a covector
• let be a vector
• s is a scalar below, where the argument of the covector is a vector:

Appendix A

The inner product between a vector x and a covector y is invariant under all transformations.

The changes to the components of the vector all change in one way and the components of the covector all change in another such that the changes will balance out.