If is the point set of an affine space, then every affine transformation on can be represented as the composition of a linear transformation on and a translation of . Unlike a purely linear transformation, an affine transformation need not preserve the origin of the affine space. Thus, every linear transformation is affine, but not every affine transformation is linear.
If is the point set of an affine space then every affine transformation on can be represented as the composition of a linear transformation on and a translation of?  Unlike a purely linear transformation an affine transformation need no!t preserve the origin of the affine space Thus every linear transformation is affine but not every affine transformation is linear