In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes...
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means that, for two vector spaces over a given field and with the same dimension, the properties that depend only on the vector-space structure are exactly...
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is the manifold's dimension. For connected differentiable manifolds, the dimension is also the dimension of the tangent vector space at any point. In geometric...
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Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space...
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Basis (linear algebra) (redirect from Linear Algebra/Basis for a Vector Space)
finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces. A basis B of a vector space V over...
34 KB (4,730 words) - 00:00, 25 September 2023
page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis. Notation. Let F denote...
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by more specific terms. Any field K {\displaystyle K} is a one-dimensional vector space over itself. The projective line over K , {\displaystyle K,} denoted...
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projective space of dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space V of dimension n + 1...
37 KB (5,658 words) - 15:29, 9 February 2024
In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization...
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The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented...
14 KB (1,863 words) - 05:01, 7 November 2023