Degenerate bilinear form
Symmetric nondegenerate forms are important generalizations of inner products, in that often all that is required is that the mapThere is the closely related notion of a unimodular form and a perfect pairing; these agree over fields but not over general rings.Symmetric nondegenerate forms are important generalizations of inner products, in that often all that is required is that the mapGeometrically, an isotropic line of the quadratic form corresponds to a point of the associated quadric hypersurface in projective space.Such a line is additionally isotropic for the bilinear form if and only if the corresponding point is a singularity.