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In mathematics, the linear span (also called the linear hull [1] or just span) of a set of elements of a vector space is the smallest linear subspace of that contains . It is the set of all finite linear combinations of the elements of S , [ 2 ] and the intersection of all linear subspaces that contain S . {\displaystyle S.}
Leon, Steven J. (2006), Linear Algebra With Applications (7th ed.), Pearson Prentice Hall Meyer, Carl D. (February 15, 2001), Matrix Analysis and Applied Linear Algebra , Society for Industrial and Applied Mathematics (SIAM), ISBN 978-0-89871-454-8 , archived from the original on March 1, 2001
In linear algebra, the closure of a non-empty subset of a vector space (under vector-space operations, that is, addition and scalar multiplication) is the linear span of this subset. It is a vector space by the preceding general result, and it can be proved easily that is the set of linear combinations of elements of the subset.
Then this map is a linear embedding of TVSs (that is, it is a linear map that is also a topological embedding) whose image (or "range") is closed in its codomain; said differently, the topology on () is identical to the subspace topology it inherits from (), and also () is a closed subset of ().
tends to 0 when n → ∞, where F n is the linear span of the basis vectors e m for m ≥ n. The unit vector basis for ℓ p, 1 < p < ∞, or for c 0, is shrinking. It is not shrinking in ℓ 1: if f is the bounded linear functional on ℓ 1 given by
Span (unit), the width of a human hand; Span (engineering), a section between two intermediate supports; Wingspan, the distance between the wingtips of a bird or aircraft; Sorbitan esters, also known as a spans; Nebbiolo, an Italian wine grape also known as Span
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