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.
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
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References in periodicals archive ?
A set has properties of an abstract mathematical object called abstract vector space. Sets of all physically logical solutions of linear and wave differential equations always form vector spaces, and their vectors are definable complex functions of space and time.
In a series of sections with plenty of examples and exercises they describe vectors, matrices and linear transformations, the solution set of a linear system, the image of a line translation, determinants, the Eigenvalue problem and Eigenvectors, and abstract vector spaces. Although intended for classroom use, this could also serve as a self-study text.