More generally, a Clifford algebra can be constructed from any vector space V equipped with a (nondegenerate) quadratic form, such as Euclidean space with its standard dot product or Minkowski space with its standard Lorentz metric. The space of spinors is the space of column vectors with 2 ⌊ ⌊ dim ⁡ ⁡ V / 2 ⌋ ⌋ components. The orthogonal Lie algebra (i.e., the infinitesimal "rotations") and the spin group associated to the quadratic form are both (canonically) contained in the Clifford algebra, so every Clifford algebra representation also defines a representation of the Lie algebra and the spin group. Depending on the dimension and metric signature, this realization of spinors as column vectors may be irreducible or it may decompose into a pair of so-called "half-spin" or Weyl representations. When the vector space V is four-dimensional, the algebra is described by the gamma matrices.