Sometimes, Euclidean vectors are considered without reference to a Euclidean space. In this case, a Euclidean vector is an element of a normed vector space of finite dimension over the reals, or, typically, an element of R n equipped with the dot product. This makes sense, as the addition in such a vector space acts freely and transitively on the vector space itself. That is, R n is a Euclidean space, with itself as an associated vector space, and the dot product as an inner product.