Change of Basis, DFT, and SVD

That is, the conversion from homogeneous coordinates in C to D coordinates is just a linear transformation.

For example, suppose Coords(o,D) = 〈1,2〉, Coords(⇒x ,D) = 〈3,2〉, and Coords(

⇒ y ,D)= 〈−2,3〉, and suppose Coords(p,C )= 〈2,1〉 (Figure 7.1). Then

Hc(p,D)= ⎡ ⎣ 3 −2 12 3 2

0 0 1

⎤ ⎦ · ⎡ ⎣ 21

⎤ ⎦=

⎡ ⎣ 59

⎤ ⎦ .