A perspective collineation with center and axis is a Collineation which leaves all lines through and points of invariant. Every perspective collineation is a Projective Collineation.
See also Collineation, Elation, Homology (Geometry), Projective Collineation
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 247-248, 1969.