Collineations

Some articles on collineations, collineation:

Projective Linear Group - Name - Collineations
... A related group is the collineation group, which is defined axiomatically ... A collineation is an invertible (or more generally one-to-one) map which sends collinear points to collinear points ... g of the set of lines, preserving the incidence relation, which is exactly a collineation of a space to itself ...
Projective Plane - Collineations - Homography
... (or projective transformation) of PG(2,K) is a collineation of this type of projective plane which is a linear transformation of the underlying vector space ... Another type of collineation of PG(2,K) is induced by any automorphism of K, these are called automorphic collineations ... If α is an automorphism of K, then the collineation given by (x0,x1,x2) → (x0α,x1α,x2α) is an automorphic collineation ...
Collineation - Types
... The main examples of collineations are projective linear transformations (also known as homographies) and automorphic collineations ... of projective geometry states that all collineations are a combination of these, as described below ... A duality is a collineation from a projective space onto its dual space, taking points to hyperplanes (and vice versa) and preserving incidence ...