![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/7/70/Basis_for_a_plane.svg/640px-Basis_for_a_plane.svg.png&w=640&q=50)
Linear span
In linear algebra, generated subspace / From Wikipedia, the free encyclopedia
In mathematics, the linear span (also called the linear hull[1] or just span) of a set S of vectors (from a vector space), denoted span(S),[2] is defined as the set of all linear combinations of the vectors in S.[3] For example, two linearly independent vectors span a plane. The linear span can be characterized either as the intersection of all linear subspaces that contain S, or as the smallest subspace containing S. The linear span of a set of vectors is therefore a vector space itself. Spans can be generalized to matroids and modules.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/7/70/Basis_for_a_plane.svg/320px-Basis_for_a_plane.svg.png)
To express that a vector space V is a linear span of a subset S, one commonly uses the following phrases—either: S spans V, S is a spanning set of V, V is spanned/generated by S, or S is a generator or generator set of V.