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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.}
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 ().
In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the image or range of the corresponding matrix transformation .
There is a trivial span A ← A → B, where the left map is the identity on A, and the right map is the given map φ. If M is a model category , with W the set of weak equivalences , then the spans of the form X ← Y → Z , {\displaystyle X\leftarrow Y\rightarrow Z,} where the left morphism is in W, can be considered a generalised morphism ...
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.
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
Download as PDF; Printable version; In other projects ... This is an outline of topics related to linear algebra, the branch of mathematics concerning linear ...
The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz .