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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.}
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 .
A linear subspace is a vector space for the induced addition and scalar multiplication; this means that the closure property implies that the axioms of a vector space are satisfied. [11] The closure property also implies that every intersection of linear subspaces is a linear subspace. [11] Linear span
Linear algebra is the branch of mathematics concerning linear equations such as: ... The concepts of linear independence, span, basis, and linear maps ...
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 .
the linear span in a vector space (also often denoted Span(S)), the generated subgroup in a group, the generated ideal in a ring, the generated submodule in a module. 2. Often used, mainly in physics, for denoting an expected value. In probability theory, () is generally used instead of .
linear form A linear map from a vector space to its field of scalars [8] linear independence Property of being not linearly dependent. [9] linear map A function between vector space s which respects addition and scalar multiplication. linear transformation A linear map whose domain and codomain are equal; it is generally supposed to be invertible.
SL – special linear group. SO – special orthogonal group. SOC – second order condition. Soln – solution. Sp – symplectic group. Sp – trace of a matrix, from the German "spur" used for the trace. sp, span – linear span of a set of vectors. (Also written with angle brackets.) Spec – spectrum of a ring. Spin – spin group.
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