# vector space

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## vector space

n.
A system consisting of a set of generalized vectors and a field of scalars, having the same rules for vector addition and scalar multiplication as physical vectors and scalars.

## vector space

n
(Mathematics) maths a mathematical structure consisting of a set of objects (vectors) associated with a field of objects (scalars), such that the set constitutes an Abelian group and a further operation, scalar multiplication, is defined in which the product of a scalar and a vector is a vector. See also scalar multiplication
References in periodicals archive ?
(Browder ) Let K be a nonempty compact convex subset of a topological vector space. Let T be a map of K into [2.sup.K], where for each x [member of] K, T(x) is a nonempty convex subset of K.
(C) There is an isomorphism between the Clifford algebra Cl(d) in d-dimensions and the exterior algebra [LAMBDA] x M of cotangent bundle [T.sup.*] M over M [9, 10] (the space of the Clifford algebra Cl(d) is isomorphic, as a vector space, to the vector space of the exterior algebra [LAMBDA] x M.
founder and CEO John Garvey joins Vector Space Systems as chief technology officer.
Micro satellite space launch enterprise Vector Space Systems has secured more than USD1 million in angel funding at Space 2.0 in Silicon Valley, the company said.
The SPA specifies a method for implementing high-level cognitive systems and behaviors in a high-dimensional vector space representation, and the NEF specifies methods for implementing vector space representations in spiking neurons.
They employed two different vector space models to interpret word meaning--a basic bag-of-words model and a slightly simplified variant of the contextualization model of Thater et al.
Let (V,+,.) be any vector space over a field K and let V (I) = < V [union] I > be a neutrosophic set generated by V and I.
Let V be a real vector space of dimension n, equipped with a basis [DELTA] = {[[alpha].sub.1], [[alpha].sub.2], ..., [[alpha].sub.n]}.
Let X be real topological vector space whose topology is induced by translation invariant metric d with the property
Definition 2 Let [F.sup.n] be a vector space over the field F, and x, y [member of] [F.sup.n] where x = [x.sub.1],[x.sub.2] ...
Let V be a n dimensional vector space over a field F and [sigma] a linear transformation on V.

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