Linear span

In linear algebra, the linear span (also called the linear hull or just span) of a set of vectors in a vector space is the intersection of all linear subspaces which each contain every vector in that set. The linear span of a set of vectors is therefore a vector space. Spans can be generalized to matroids and modules. For expressing that a vector space V is a span of a set S, one commonly uses the following phrases: S spans V; V is spanned by S; S is a spanning set of V; S is a generating set of V.