Velocity addition u ⊕ v corresponds to the composition of boosts B (v) B (u) in that order. The B (u) acts on X first, then B (v) acts on B (u) X. Notice succeeding operators act on the left in any composition of operators, so B (v) B (u) should be interpreted as a boost with velocities u then v, not v then u. Performing the Lorentz transformations by block matrix multiplication,