The standard Lorentzian inner product on R^4 is given by -d x_0^2 + d x_1^2 + d x_2^2 + d x_3^2, i.e., for vectors v = (v_0, v_1, v_2, v_3) and w = (w_0, w_1, w_2, w_3), 〈v, w〉 = - v_0 w_0 + v_1 w_1 + v_2 w_2 + v_3 w_3. R^4 endowed with the metric tensor induced by the above Lorentzian inner product is known as Minkowski space and is denoted R^(1, 3).
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