Vector Field

We create a vector field by defining a Subspace of our space and then every point in the Subspace corresponds to a vector.

As an example, we might look a subspace be all the points on the unit circle, and then vector for a point is the tangent Vector for that point.

Appendix A

You might guess that we could make a different kind of field by replacing the vectors with something else.

You would be right.

We could Define our Subspace read the unit circle and for every point (1, theta), we attach the 2×2 matrix that will perform a counterclockwise rotation of theta.