 This generates a basis of one scalar formula_9, four vectors formula_10, six bivectors formula_11, four pseudovectors formula_12 and one pseudoscalar formula_13, where formula_14.Associated with the orthogonal basis formula_15 is the reciprocal basis formula_16 for 
formula_17, satisfying the relation
These reciprocal frame vectors differ only by a sign, with formula_19, and formula_20 for formula_21.A vector may be represented in either upper or lower index coordinates formula_22 with summation over formula_17, according to the Einstein notation, where the coordinates may be extracted by taking dot products with the basis vectors or their reciprocals.