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vector space

noun, Mathematics
1.
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.
Also called linear space.
Origin
1940-1945
1940-45
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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British Dictionary definitions for vector-space

vector space

noun
1.
(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 & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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vector-space in Science
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 © 2002. Published by Houghton Mifflin. All rights reserved.
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