Collineation

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. All projective linear transformations induce a collineation. A collineation of a projective space to itself is also called an automorphism, and the set of all collineations of a space to itself form a group, called the collineation group.