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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
References
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 247-248, 1969.