As an example, let the vector v = ( v 1 , v 2 ) ∈ ∈ R 2 , be a vector in the plane. A rotation of the vector through an angle θ in counterclockwise direction is given by the rotation matrix : R = ( cos ⁡ ⁡ θ θ − − sin ⁡ ⁡ θ θ sin ⁡ ⁡ θ θ cos ⁡ ⁡ θ θ ) , which can be viewed either as an active transformation or a passive transformation (where the above matrix will be inverted), as described below.