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linearly dependent subset

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  • Basis (linear algebra) — Basis vector redirects here. For basis vector in the context of crystals, see crystal structure. For a more general concept in physics, see frame of reference. In linear algebra, a basis is a set of linearly independent vectors that, in a linear… …   Wikipedia

  • Linear independence — In linear algebra, a family of vectors is linearly independent if none of them can be written as a linear combination of finitely many other vectors in the collection. A family of vectors which is not linearly independent is called linearly… …   Wikipedia

  • Matroid — In combinatorics, a branch of mathematics, a matroid (  /ˈmeɪ …   Wikipedia

  • Euclidean subspace — In linear algebra, an Euclidean subspace (or subspace of R n ) is a set of vectors that is closed under addition and scalar multiplication. Geometrically, a subspace is a flat in n dimensional Euclidean space that passes through the origin.… …   Wikipedia

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

  • Determinant — This article is about determinants in mathematics. For determinants in epidemiology, see Risk factor. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific… …   Wikipedia

  • Set system of finite character — A family mathcal{F} of sets is of finite character provided it has the following properties: #For each Ain mathcal{F}, every finite subset of A belongs to mathcal{F}. #If every finite subset of a given set A belongs to mathcal{F}, then A belongs… …   Wikipedia

  • Dimension theorem for vector spaces — In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite, or given by an infinite cardinal number, and defines the dimension of the space.… …   Wikipedia

  • Indexed family — In mathematics, an indexed family of sets is defined in stages, beginning with the more general concept of an indexed family of elements, which is really just an alternative way of conceptualizing a function or a mapping.First, a mapping f from a …   Wikipedia

  • Affine transformation — In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis , connected with ) between two vector spaces (strictly speaking, two affine spaces) consists of a linear transformation followed by a translation::x… …   Wikipedia

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