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Alexander.zw (talk | contribs) Add the example of the span of the empty set |
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In [[linear algebra]], the '''linear span''' (also called the '''linear hull''' or just '''span''') of a [[Set (mathematics)|set]] of [[vector space|vectors]] in a [[vector space]] is the [[intersection (set theory)|intersection]] of all [[linear subspace]]s 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 [[matroid]]s and [[Module (mathematics)|modules]].
For expressing that a vector space {{mvar|V}} is a span of a set {{mvar|S}}, one commonly uses the following phrases: {{mvar|S}} spans {{mvar|V}}; {{mvar|V}} is spanned by {{mvar|S}}; {{mvar|S}} is a '''spanning set''' of {{mvar|V}}; {{mvar|S}} is a generating set of {{mvar|V}}.
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