Central collineation
Definition
A collineation of a projective plane is termed a central collineation if it satisfies the following equivalent conditions:
- It has a center, i.e., a point such that all the lines through that point are preserved (as lines) by the collineation.
- 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. For full proof, refer: non-identity collineation has center iff it has axis and both are unique