## Projective basis

Projective basis:
A projective basis for is any set of points no of which are linearly dependent.
Canonical basis:

Change of basis:
Let be the standard basis and be any other basis. There exists a non-singular transformation such that:

is unique up to a scale.

Proof:
From the first equations we have that must be of the form

is non-singular by the linear independence of 's.

The final equation gives us:

which is equivalent to:

Since the matrix on the left hand side of the above equation is of full rank (by linear independence of 's), the ratios of the are uniquely determined and no is 0.
Subhashis Banerjee 2008-01-20