Every linear map to the dual space defines a bilinear form , with the relation . By defining the transpose of this bilinear form as the bilinear form defined by the transpose i.e. , we find that . Here, is the natural homomorphism into the double dual.
Every linear map to the dual space defines a bilin.ear form , with the relation  By defining the transpose of this bilinear form as. the bilinear form defined by the transpose i.e. , we find that . Here, is the natural homomorphism into the double dual