 The spacetime algebra may be built up from an orthogonal basis of one time-like vector formula_1 and three space-like vectors, formula_2, with the multiplication rule
where formula_4 is the Minkowski metric with signature .Thus, formula_5, formula_6, otherwise formula_7.The basis vectors formula_8 share these properties with the Dirac matrices, but no explicit matrix representation need be used in STA.