Coordinate space F n can be equipped with the standard dot product : ⟨ ⟨ x , y ⟩ ⟩ = x ⋅ ⋅ y = x 1 y 1 + ⋯ ⋯ + x n y n . In R 2 , this reflects the common notion of the angle between two vectors x and y , by the law of cosines : x ⋅ ⋅ y = cos ⁡ ⁡ ( ∠ ∠ ( x , y ) ) ⋅ ⋅ | x | ⋅ ⋅ | y | . Because of this, two vectors satisfying ⟨ ⟨ x , y ⟩ ⟩ = 0 are called orthogonal. An important variant of the standard dot product is used in Minkowski space : R 4 endowed with the Lorentz product ⟨ ⟨ x | y ⟩ ⟩ = x 1 y 1 + x 2 y 2 + x 3 y 3 − − x 4 y 4 . In contrast to the standard dot product, it is not positive definite : ⟨ ⟨ x | x ⟩ ⟩ also takes negative values, for example, for x = ( 0 , 0 , 0 , 1 ) . Singling out the fourth coordinate— corresponding to time, as opposed to three space-dimensions—makes it useful for the mathematical treatment of special relativity. Note that in other conventions time is often written as the first, or "zeroeth" component so that the Lorentz product is written ⟨ ⟨ x | y ⟩ ⟩ = − − x 0 y 0 + x 1 y 1 + x 2 y 2 + x 3 y 3 .