The magnitude differences are not relevant however as scores remain proper under affine transformation.

All such parameterizations are related through an affine transformation .

Point reflection can be classified as an affine transformation.

Finally gets transformed by the private affine transformation to , the valid signature.

We thus consider a point and the transformed point , where A is an affine transformation.

A translation is an affine transformation with no fixed points.

An affine transformation is equivalent to a linear transformation followed by a translation.

This is because the horseshoe maps the left cap into itself by an affine transformation that has exactly one fixed point.

It is also the first proof to explicitly use an affine transformation to set up a convenient coordinate system.

Sometimes each function is required to be a linear, or more generally an affine transformation and hence represented by a matrix.