The Euclidean space R n is often presented as the Euclidean space of dimension n. This is motivated by the fact that every Euclidean space of dimension n is isomorphic to the Euclidean space R n . More precisely, given such a Euclidean space, one may choose any point O as an origin. By Gram–Schmidt process, one may also find an orthonormal basis of the associated vector space (a basis such that the inner product of two basis vectors is 0 if they are different and 1 if they are equal). This defines Cartesian coordinates of any point P of the space, as the coordinates on this basis of the vector O P → → . These choices define an isomorphism of the given Euclidean space onto R n , by mapping any point to the n -tuple of its Cartesian coordinates, and every vector to its coordinate vector.