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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. Vector space - Wikipedia

    en.wikipedia.org/wiki/Vector_space

    The closure property also implies that every intersection of linear subspaces is a linear subspace. [11] Linear span Given a subset G of a vector space V, the linear span or simply the span of G is the smallest linear subspace of V that contains G, in the sense that it is the intersection of all linear subspaces that contain G.

  5. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    Linear algebra is the branch of mathematics concerning linear equations such as ... For example, given a linear map T : ... The concepts of linear independence, span, ...

  6. 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.

  7. Rank (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Rank_(linear_algebra)

    The equivalence of determinantal rank and column rank is a strengthening of the statement that if the span of n vectors has dimension p, then p of those vectors span the space (equivalently, that one can choose a spanning set that is a subset of the vectors): the equivalence implies that a subset of the rows and a subset of the columns ...