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The general case of a collineation
be rewritten in inhomogeneous affine coordinates as:
Property: A translation in affine space corresponds to a collineation leaving each
point at infinity invariant.
Proof: The translation
can be represented by the matrix:
More generally, any affine transformation is a collineation, because it can be
decomposed into a linear mapping and a translation:
In homogeneous coordinates, this becomes:
Prove that a collineation is an affine transformation if and only if it
maps the hyperplane at infinity xn+1=0 into itself (i.e. all
points at infinity are mapped onto points at infinity).