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title: Spans
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## Spans

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##### Introduction
Let S be a nonempty subset of a vector space V. The span of S, denoted by span(S), is the set containing of all linear combinations of vectors in S. For convenience, we define span(∅)={0}.

or

Let S be a set of vectors in a vector space W. The subspace spanned by S is defined to be intersection W of all subspaces of V which contain S. When S is finite set of vectors, S={α1,α2,...,αn}, we shall simply call W the subspace spanned by the vectors α1,α2,...,αn.

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