Correlation (projective geometry)

Correlation (projective geometry)

A correlation is a duality (collineation from a projective space onto its dual space, taking points to hyperplanes (and vice versa) and preserving incidence) from a projective space to itself. In the case of projective planes correlations can only exist if the plane is self-dual.

If a correlation σ is involutory (that is, two applications of the correlation equals the identity: σ²(P)=P for all points P) then it is called a polarity.