If a Lorentz covariant 4-vector is measured in one inertial frame with result X , and the same measurement made in another inertial frame (with the same orientation and origin) gives result X ′ , the two results will be related by X ′ = B ( v ) X where the boost matrix B ( v ) represents the rotation-free Lorentz transformation between the unprimed and primed frames and v is the velocity of the primed frame as seen from the unprimed frame. The matrix is given by B ( v ) = [ γ γ − − γ γ v x / c − − γ γ v y / c − − γ γ v z / c − − γ γ v x / c 1 + ( γ γ − − 1 ) v x 2 v 2 ( γ γ − − 1 ) v x v y v 2 ( γ γ − − 1 ) v x v z v 2 − − γ γ v y / c ( γ γ − − 1 ) v y v x v 2 1 + ( γ γ − − 1 ) v y 2 v 2 ( γ γ − − 1 ) v y v z v 2 − − γ γ v z / c ( γ γ − − 1 ) v z v x v 2 ( γ γ − − 1 ) v z v y v 2 1 + ( γ γ − − 1 ) v z 2 v 2 ] = [ γ γ − − γ γ β β → → T − − γ γ β β → → I + ( γ γ − − 1 ) β β → → β β → → T β β 2 ] ,