A tangent vector at a point p may be defined, here specialized to Cartesian coordinates in Lorentz frames, as 4 × 1 column vectors v associated to each Lorentz frame related by Lorentz transformation Λ such that the vector v in a frame related to some frame by Λ transforms according to v → Λ v. This is the same way in which the coordinates x transform. Explicitly, x ′ μ μ = Λ Λ μ μ ν ν x ν ν , v ′ μ μ = Λ Λ μ μ ν ν v ν ν .