Orthogonality

Abstract

This last chapter deals with a particular case of dualized geometries, when the set of closed hyperplanes is given by a polarity. The so obtained orthogeometries can be equivalently described by an orthogonality relation ┴, as shown in Section 14.1. The typical example of an orthogeometry is the projective geometry associated to a vector space equipped with a non-singular reflexive sesquilinear form. Moreover, one can choose either an alternating bilinear form or a Hermitian form.