vector space

(redirected from Real 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 ?
A scalar product or inner product on a real vector space V is a positive definite symmetric bilinear form < , > : V x V [right arrow] R, which means for x,y,z [member of] V and [lambda] [member of] R, the following requirements are fulfilled:
Krause presents a systematic, rigorous, and self-contained treatment of positive dynamical systems based on analyzing the iteration of nonlinear self-mappings of a convex cone in some real vector space.
In [2], Abardia and Bernig studied projection bodies in complex vector spaces: The real vector space V of real dimension n is replaced by a complex vector space W of complex dimension m and the group SL(V) = SL(n, R) is replaced by the group SL(W,C) = SL(m,C).
We fix a d-dimensional real vector space U and a lattice [LAMBDA] [subset or equal to] U.
1] be the three-dimensional Minkowski space, that is, the three-dimensional real vector space [E.
Real vector space structure ([parallel]G[parallel], [direct sum], [cross product]) for the set [parallel]G[parallel] of onedimensional "vectors"
Suppose X is a real vector space with dim X [greater than or equal to] 2 and [perpendicular to] is a binary relation on X with the following properties:
Let V be a real vector space of dimension n, equipped with a basis [DELTA] = {[[alpha].