A collineation is a bijection from a projective space to a projective space of the same finite dimension which preserves the inclusions of subspaces. Equivalently, it is often defined by a seemingly weaker condition, which is also used in the infinite-dimensional case: a collineation is a bijection of projective spaces which sends each triple of collinear points into a triple of collinear points.
A projective collineation is a collineation such that its restriction to every projective hyperplane is a projective isomorphism.
A perspective collineation is a (projective) collineation from a projective plane to itself such that the restriction to one, and hence to any projective line is a perspectivity onto its image line.
Similarly, a correlation is a bijection from a projective space to a projective space of the same finite dimension which reverses the inclusions of subspaces.
The terms collineation and correlation have been introduced into projective geometry by Moebius in 1827.
Last revised on May 18, 2016 at 12:12:08. See the history of this page for a list of all contributions to it.