**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

**vector space** — Math. an additive group in which addition is commutative and with which is associated a field of scalars, as the field of real numbers, such that the product of a scalar and an element of the group or a vector is defined, the product of two… … Universalium

**vector space** — noun a) A type of set of vectors that satisfies a specific group of constraints. A vector space is a set of vectors which can be linearly combined. b) A set V, whose elements are called vectors , together with a binary operation + forming a… … Wiktionary

**vector space** — vektorinė erdvė statusas T sritis fizika atitikmenys: angl. vector space vok. Vektorraum, m rus. векторное пространство, n pranc. espace vectoriel, m … Fizikos terminų žodynas

**Vector space model** — (or term vector model ) is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers, such as, for example, index terms. It is used in information filtering, information retrieval, indexing and… … Wikipedia

**vector space** — noun Date: 1937 a set of vectors along with operations of addition and multiplication such that the set is a commutative group under addition, it includes a multiplicative inverse, and multiplication by scalars is both associative and… … New Collegiate Dictionary

**vector space** — noun : a set representing a generalization of a system of vectors and consisting of elements which comprise a commutative group under addition, each of which is left unchanged under multiplication by the multiplicative identity of a field, and… … Useful english dictionary

**Topological vector space** — In mathematics, a topological vector space is one of the basic structures investigated in functional analysis. As the name suggests the space blends a topological structure (a uniform structure to be precise) with the algebraic concept of a… … Wikipedia

**Normed vector space** — In mathematics, with 2 or 3 dimensional vectors with real valued entries, the idea of the length of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of vector length are crucial. 1. The zero… … Wikipedia

**Locally convex topological vector space** — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… … Wikipedia