A nonempty subset "W" of a vector space "V" that is closed under addition and scalar multiplication (and therefore contains the 0-vector of "V") is called a "linear subspace" of "V", or simply a "subspace" of "V", when the ambient space is unambiguously a vector space. Subspaces of "V" are vector spaces (over the same field) in their own right. The intersection of all subspaces containing a given set "S" of vectors is called its span, and it is the smallest subspace of "V" containing the set "S". Expressed in terms of elements, the span is the subspace consisting of all the linear combinations of elements of "S".