A transformation of the plane which transforms collinear points into collinear points. A projective collineation transforms every one-dimensional 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 geometric homology they are not. For further discussion, see Coxeter (1969, p. 248).

See also

Affine Transformation, Connex, Correlation, Elation, Equiaffinity, Geometric Homology, Perspective Collineation, Projective Collineation

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Coxeter, H. S. M. "Collineations and Correlations." §14.6 in Introduction to Geometry, 2nd ed. New York: Wiley, pp. 247-251, 1969.

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Cite this as:

Weisstein, Eric W. "Collineation." From MathWorld--A Wolfram Web Resource.

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