Consider two inertial frams O and O', with O' moving along the x axis of O with a constant speedIn O events A and B occur with spacetime coordinatesandrespectively.

The vector in 4 dimensional spacetime from A to B in O isand the components of velocity in O areandThe Lorentz transformation fromin O toin O' is

In O' the components of velocity are

The inverse transformation from O' to O is obtained by changing the sign ofand interchangingandandandandand