Change of Basis in 2D

Given a point in the plane you can see its coordinates with respect to the standard basis , or compute its coordinates with respect to a different basis . The signed area of the parallelogram determined by this basis, , is a crucial quantity.

This Demonstration complements the Demonstration "Coordinates of a Point Relative to a Basis in 2D", by E. Schulz, which shows how a point varies as its coordinates change.