In
projective geometry, a
collineation is a one-to-one and onto map (a
bijection) from one
projective space to another, or from a projective space to itself, such that the images of
collinear points are themselves collinear. A collineation is thus an
isomorphism between projective spaces, or an
automorphism from a projective space to itself. Some authors restrict the definition of collineation to the case where it is an automorphism. The set of all collineations of a space to itself form a
group, called the
collineation group.