Page 99 - Computer Graphics Handout

3.3.3 Example Change of Representation
Suppose that we have a vector w whose representation in some basis is

We can denote the three basis vectors as v1, v2, and v3. Hence,
w = v1+ 2v2+ 3v3.
Now suppose that we want to make a new basis from the three vectors v1, v2, and v3
where
u1= v1,u2= v1+ v2,u3= v1+ v2+ v3.
The matrix M is

The matrix that converts a representation in v1, v2, and v3 to one in which the basis
vectors are u1, u2, and u3 is
T −1
T = (M )

In the new system, the representation of w is

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