definitions

vector space

noun Mathematics.

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 scalars times a vector is associative, one times a vector is the vector, and two distributive laws hold.

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Nearby words

vector field, vector font, vector function, vector graphic, vector product, vector space, vector sum, vectorcardiogram, vectorcardiography, vectorial, vectorially

Origin of vector space

First recorded in 1940–45
Also called linear space.
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

British Dictionary definitions for vector space

vector space

noun

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 vectorSee also scalar multiplication
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Science definitions for vector space

vector space

A set of generalized vectors and a field of scalars, together with rules for their addition and multiplication (the same rules used for ordinary vectors and scalars).
The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.