In viewing a tensor as a multilinear map, it is conventional to identify the double dual V of the vector space V, i.e., the space of linear functionals on the dual vector space V, with the vector space V. There is always a natural linear map from V to its double dual, given by evaluating a linear form in V against a vector in V. This linear mapping is an isomorphism in finite dimensions, and it is often then expedient to identify V with its double dual.