 This notion does not require the specification of an inner product on "V".In finite dimensions, the two notions of dual cone are essentially the same because every finite dimensional linear functional is continuous, and every continuous linear functional in a inner product space induces a linear isomorphism (nonsingular linear map) from "V*" to "V", and this isomorphism will take the dual cone given by the second definition, in "V*", onto the one given by the first definition; see the Riesz representation theorem.If "C" is equal to its dual cone, then "C" is called self-dual.