• Thumbnail for Vector space
    In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied...
    87 KB (11,487 words) - 18:57, 28 October 2024
  • Thumbnail for Dimension (vector space)
    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...
    9 KB (1,485 words) - 09:34, 2 November 2024
  • Thumbnail for Normed vector space
    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...
    18 KB (2,890 words) - 22:11, 21 February 2024
  • Vector space model or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the distance...
    10 KB (1,415 words) - 01:57, 30 September 2024
  • Thumbnail for Basis (linear algebra)
    In mathematics, a set B of vectors in a vector space V is called a basis (pl.: bases) if every element of V may be written in a unique way as a finite...
    34 KB (4,749 words) - 01:17, 16 October 2024
  • A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar...
    103 KB (13,537 words) - 12:47, 4 October 2024
  • Thumbnail for Inner product space
    mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an...
    56 KB (7,307 words) - 12:28, 12 November 2024
  • This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis. Notation...
    15 KB (2,119 words) - 22:37, 30 November 2023
  • In mathematics, a super vector space is a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded vector space, that is, a vector space over a field K {\displaystyle...
    11 KB (1,893 words) - 21:49, 26 August 2022
  • a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct...
    6 KB (884 words) - 13:58, 30 September 2024
  • In mathematics, a symplectic vector space is a vector space V {\displaystyle V} over a field F {\displaystyle F} (for example the real numbers R {\displaystyle...
    15 KB (2,275 words) - 11:50, 14 August 2024
  • on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is called...
    10 KB (2,694 words) - 01:12, 24 October 2024
  • Thumbnail for Euclidean space
    re-formalized to define Euclidean spaces through axiomatic theory. Another definition of Euclidean spaces by means of vector spaces and linear algebra has been...
    47 KB (6,964 words) - 20:52, 7 November 2024
  • In mathematics, any vector space V {\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms...
    45 KB (6,872 words) - 18:21, 24 June 2024
  • In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance...
    36 KB (5,957 words) - 16:18, 5 November 2024
  • transformation, vector space homomorphism, or in some contexts linear function) is a mapping V → W {\displaystyle V\to W} between two vector spaces that preserves...
    43 KB (7,001 words) - 19:46, 25 October 2024
  • functional analysis, a Banach space (pronounced [ˈbanax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows...
    104 KB (17,224 words) - 06:29, 3 October 2024
  • Thumbnail for Orientation (vector space)
    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...
    15 KB (1,988 words) - 06:09, 7 October 2024
  • Thumbnail for Affine space
    point, the zero vector is called the origin. Adding a fixed vector to the elements of a linear subspace (vector subspace) of a vector space produces an affine...
    48 KB (7,538 words) - 01:30, 16 October 2024
  • topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can be...
    58 KB (10,568 words) - 23:16, 10 August 2024
  • Thumbnail for Vector bundle
    mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X {\displaystyle...
    31 KB (4,089 words) - 16:41, 9 April 2024
  • Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that...
    29 KB (5,067 words) - 01:54, 15 October 2024
  • 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...
    6 KB (780 words) - 22:18, 8 February 2024
  • vector space V {\displaystyle V} by a subspace N {\displaystyle N} is a vector space obtained by "collapsing" N {\displaystyle N} to zero. The space obtained...
    11 KB (1,567 words) - 16:41, 21 November 2024
  • Thumbnail for Linear span
    linear hull or just span) of a set S {\displaystyle S} of elements of a vector space V {\displaystyle V} is the smallest linear subspace of V {\displaystyle...
    17 KB (2,433 words) - 19:15, 17 October 2024
  • product V ⊗ W {\displaystyle V\otimes W} of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V × W...
    50 KB (8,640 words) - 13:51, 17 October 2024
  • mathematics, the complex conjugate of a complex vector space V {\displaystyle V\,} is a complex vector space V ¯ {\displaystyle {\overline {V}}} that has...
    6 KB (860 words) - 16:01, 12 December 2023
  • analytic geometry. In condensed mathematics, liquid vector spaces are alternatives to topological vector spaces. A condensed set is a sheaf of sets on the site...
    7 KB (700 words) - 14:25, 27 October 2024
  • Thumbnail for Tensor
    sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There...
    69 KB (9,351 words) - 11:28, 12 October 2024
  • depth. Suppose V and W are vector spaces over the field K. The cartesian product V × W can be given the structure of a vector space over K (Halmos 1974, §18)...
    22 KB (3,580 words) - 16:29, 14 May 2024