If a frame F ′ is boosted with velocity u relative to frame F, and another frame F ′′ is boosted with velocity v relative to F ′, the separate boosts are X ″ = B ( v ) X ′ , X ′ = B ( u ) X and the composition of the two boosts connects the coordinates in F ′′ and F, X ″ = B ( v ) B ( u ) X . Successive transformations act on the left. If u and v are collinear (parallel or antiparallel along the same line of relative motion), the boost matrices commute : B (v) B (u) = B (u) B (v). This composite transformation happens to be another boost, B (w), where w is collinear with u and v.