Collineation

Summary

A collineation is a bijection between the points of two geometries that maps lines onto lines. It is the notion of isomorphism for projective geometries and other incidence structures. Every projective transformation of a projective space of dimension at least $2$ is a collineation. The fundamental theorem of projective geometry says that all collineations come from semilinear maps. The collineations of a geometry form its collineation group, its group of symmetries.