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).

# Collineation

## See also

Affine Transformation, Connex, Correlation, Elation, Equiaffinity, Geometric Homology, Perspective Collineation, Projective Collineation## Explore with Wolfram|Alpha

## References

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

## Referenced on Wolfram|Alpha

Collineation## Cite this as:

Weisstein, Eric W. "Collineation." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Collineation.html