\begin{matrix} x'^{α} = Λ_{β}^{α} x^{β} + a^{α} \\ γ = {(1 - β^{2})}^{- \frac{1}{2}}, β = \frac{v}{c} \end{matrix}

spezielle

Λ_{0}^{0} = γ, Λ_{0}^{i} = Λ_{i}^{0} = γ \frac{v^{i}}{c}, Λ_{k}^{i} = δ_{i k} + (γ - 1) \frac{v^{i} v^{k}}{v^{2}}

Lorentz Transformation