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  2. Linear span - Wikipedia

    en.wikipedia.org/wiki/Linear_span

    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.}

  3. Row and column spaces - Wikipedia

    en.wikipedia.org/wiki/Row_and_column_spaces

    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 .

  4. Spaces of test functions and distributions - Wikipedia

    en.wikipedia.org/wiki/Spaces_of_test_functions...

    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 ().

  5. Span - Wikipedia

    en.wikipedia.org/wiki/Span

    Mathematics. Linear span, or simply span, in linear algebra; Span (category theory) ... This page was last edited on 28 December 2024, at 18:11 (UTC).

  6. Span (category theory) - Wikipedia

    en.wikipedia.org/wiki/Span_(category_theory)

    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 ...

  7. Closure (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Closure_(mathematics)

    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.

  8. Schauder basis - Wikipedia

    en.wikipedia.org/wiki/Schauder_basis

    An uncountable Schauder basis is a linearly ordered set rather than a sequence, and each sum inherits the order of its terms from this linear ordering. They can and do arise in practice. As an example, a separable Hilbert space can only have a countable Schauder basis, but a non-separable Hilbert space may have an uncountable one.

  9. Linear subspace - Wikipedia

    en.wikipedia.org/wiki/Linear_subspace

    In mathematics, and more specifically in linear algebra, a linear subspace or vector subspace [1] [note 1] is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces .

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