Applying this transformation twice on a 4-vector gives a transformation of the same form. The new symmetry of 'inversion' is given by the 3-tensor Q . This symmetry becomes Poincaré symmetry if we set Q = 0. When Q = 0 the second condition requires that O is an orthogonal matrix. This transformation is 1-1 meaning that each point is mapped to a unique point only if we theoretically include the points at infinity.