Technically, a non-degenerate bilinear form provides a map between a vector space and its dual, in this context, the map is between the tangent spaces of and the cotangent spaces of . At a point in , the tangent and cotangent spaces are dual vector spaces (so the dimension of the cotangent space at an event is also ). Just as an authentic inner product on a vector space with one argument fixed, by Riesz representation theorem, may be expressed as the action of a linear functional on the vector space, the same holds for the Minkowski inner product of Minkowski space.