# vector space

(redirected from Complex vector space)
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Related to Complex vector space: Real vector space

## 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.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## 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
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
References in periodicals archive ?
Let X be a locally convex real or complex vector space. Denote by L(X) the space of linear continuous operators on X.
The oscillations of the particle in the zeropoint field may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analysed in the complex vector formalism considering the algebra of complex null vectors.
In this framework, C is the complex vector space, [G.sub.n] is the Clifford algebra or geometric algebra associated with the n-dimensional real space [V.sup.n], and [dot in a circle]: ([Real part] x [cross product]) is the new generalized geometric product.
Complex numbers are sets that represent possible physical states and form an abstract complex vector space of growth and increment.
A quantum bit, or qubit, is a unit vector in a two-dimensional complex vector space for which a particular basis, denoted by {|0>, |1>}, has been fixed.
In fact, let L be any nondegenerate inner product on a real or complex vector space. We claim that L restricted to any generic subspace is also nondegenerate.
The aim of this article is to explore the structure of the photon in complex vector space. To understand the structure of the photon, the electromagnetic field is expressed as a complex vector and the total energy momentum even multivector is developed in section 2.
In , 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).
By a Hermitian structure on [C.sup.2] we mean any Hermitian product (definite or indefinite) G on the complex vector space [C.sup.2].
If A [member of] [0, +[infinity]), we denote by [H.sub.b(s,m(r;q))] ([B.sub.1/A](0)) the complex vector space of all f [member of] H ([B.sub.1/A] (0)) such that [[??].sup.j]f (0) [member of] [P.sub.(s,m(r;q))] ([sup.j]E), for all j [member of] N and
Beginning chapters cover mathematical preliminaries (complex numbers and complex vector spaces), and present the basic architecture of quantum computing.

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