Duality Mappings and Metric Extensor

We introduce the key concepts of duality mappings and metric extensor. The fundamental identities involving the duality mappings are presented, and we disclose the logical equivalence between the so-called metric tensor and the metric extensor. By making use of the duality mappings and the metric extensor, we construct the so-called metric products, i.e., scalar product and contracted products of both multivectors and multiforms. The so-known identities involving the metric products are obtained. We find the fundamental formulas involving the metric extensor and, specially, we try its surprising inversion formula. This proposal unveils, once and for all, an unsuspected meaning of the metric products.