In the (+−−−) metric signature, evaluating the summation over indices gives: A ⋅ ⋅ B = A 0 B 0 − − A 1 B 1 − − A 2 B 2 − − A 3 B 3 while in matrix form: A ⋅ ⋅ B = ( A 0 A 1 A 2 A 3 ) ( 1 0 0 0 0 − − 1 0 0 0 0 − − 1 0 0 0 0 − − 1 ) ( B 0 B 1 B 2 B 3 )