collineation
Noun
Meaning
The act of aiming at, or directing in a line with, a fixed object.
Source: Webster's dictionarySynonyms
Phrases with the word
Examples
A permutation of the seven points that carries collinear points (points on the same line) to collinear points is called a collineation or symmetry of the plane.
If a correlation φ is not a polarity then φ 2 is a nontrivial collineation.
Another type of collineation of PG(2,K) is induced by any automorphism of K, these are called automorphic collineations.
The affine planes formed by the removal of different lines of the projective plane will be isomorphic if and only if the removed lines are in the same orbit of the collineation group of the projective plane.
The collection of fixed points and fixed lines of a collineation form a closed configuration, which is a system of points and lines that satisfy the first two but not necessarily the third condition in the definition of a projective plane.
Thus, the fixed point and fixed line structure for any collineation either form a projective plane by themselves, or a degenerate plane.