Then without rotations, the matrix Λ has components given by: Λ Λ 00 = γ γ , Λ Λ 0 i = Λ Λ i 0 = − − γ γ β β i , Λ Λ i j = Λ Λ j i = ( γ γ − − 1 ) β β i β β j β β 2 + δ δ i j = ( γ γ − − 1 ) v i v j v 2 + δ δ i j , where the Lorentz factor is defined by: γ γ = 1 1 − − β β ⋅ ⋅ β β , and δ ij is the Kronecker delta. Contrary to the case for pure rotations, the spacelike and timelike components are mixed together under boosts.