Lorentz generators can be added together, or multiplied by real numbers, to obtain more Lorentz generators. In other words, the set of all Lorentz generators V = { ζ ζ ⋅ ⋅ K + θ θ ⋅ ⋅ J } together with the operations of ordinary matrix addition and multiplication of a matrix by a number, forms a vector space over the real numbers. The generators J x, J y, J z, K x, K y, K z form a basis set of V, and the components of the axis-angle and rapidity vectors, θ x, θ y, θ z, ζ x, ζ y, ζ z, are the coordinates of a Lorentz generator with respect to this basis.