Change of Basis in 2D
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.
P
(,)
x
1
x
2
(,)
1
e
2
e
(,)
z
1
z
2
(,)
1
v
2
v
det(,)
1
v
2
v
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.