If and are not collinear but in different directions, the situation is considerably more complicated. Lorentz boosts along different directions do not commute: and are not equal. Also, each of these compositions is "not" a single boost, but they are still Lorentz transformations they each preserve the spacetime interval. It turns out the composition of any two Lorentz boosts is equivalent to a boost followed or preceded by a rotation on the spatial coordinates, in the form of or . The and are composite velocities, while and are rotation parameters (e.g. axis-angle variables, Euler angles, etc.). The rotation in block matrix form is simply