Central collineation

Definition
A collineation of a projective plane is termed a central collineation if it satisfies the following equivalent conditions:


 * 1) It has a center, i.e., a point such that all the lines through that point are preserved (as lines) by the collineation.
 * 2) It has an axis, i.e., a line such that all points on the line are preserved (as points) by the collineation.

The identity element is a central collineation, with any point permissible as a center and any line permissible as an axis. For any other central collineation, therei s a unique center and unique axis.

Relation with other properties

 * Weaker than::Elation: This is a central collineation where the center lies on the axis.
 * Weaker than::Homology: This is a central collineation where the center does not lie in the axis.