Polarity

Summary

A polarity of a projective space is a correlation of order $2$. It sends points to hyperplanes and hyperplanes to points, it reverses inclusion, and applying it twice gives the identity. Polarities are the geometric form of non-degenerate reflexive forms, such as symmetric, alternating and Hermitian forms. They underlie duality in projective geometry, the theory of pole and polar for conics, and polar spaces.