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A transformation of the plane which transforms Collinear points into Collinear points. A projective collineation transforms every 1-D form projectively, and a perspective collineation is a collineation which leaves all lines through a point and points through a line invariant. In an Elation, the center and axis are incident; in a Homology they are not. For further discussion, see Coxeter (1969, p. 248).
See also Affinity, Correlation, Elation, Equiaffinity, Homology (Geometry), Perspective Collineation, Projective Collineation
References
Coxeter, H. S. M. ``Collineations and Correlations.'' §14.6 in
Introduction to Geometry, 2nd ed. New York: Wiley, pp. 247-251, 1969.