The linear span, or span, of a set S of elements in a vector space V is the smallest linear subspace of V that contains S, equal to the set of all finite linear combinations of the elements of S. For a finite set of vectors v1 through vn, the span consists of every sum of scalar multiples lambda-1 times v1, lambda-2 times v2 and so on, where the scalars come from the vector space's underlying field. Two linearly independent vectors in three dimensional space span a plane through the origin, and the two vectors (1,0,0) and (0,1,0) span the entire xy-plane, the set of all points of the form (a, b, 0).
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Object KindStructure or Algebraic Object 1 Connections
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Source Linear Span (Wikipedia)
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1. Linear Span (Wikipedia)
Lead section
In mathematics, the linear span (also called the linear hull or just span) of a set S {\displaystyle S} of elements of a vector space V {\displaystyle V} is the smallest linear subspace of V {\displaystyle V} that contains S . {\displaystyle S.} It is the set of all finite linear combinations of the elements of S
In Branch: Linear Algebra, Lead
the linear span (also called the linear hull or just span)
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