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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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Also called linear space.

Origin:
1940–45

Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2012.
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Vector space is always a great word to know.

So is cube. Does it mean:

a system of calculation based on the properties of numbers; the discussion of a problem by algebra consisting of calculus and its higher developments

the third power of a quantity such as a cubed = a?a?a

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Collins

World English Dictionary

vector space

—n
	maths See also scalar multiplication 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

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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American Heritage

Science Dictionary

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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FOLDOC

Computing Dictionary

vector space definition

mathematics
An additive group on which some (scalar) field has an associative multiplicative action which distributes over the addition of the vector space and respects the addition of the (scalar) field: for vectors u, v and scalars h, k; h(u+v) = hu + hv; (h+k)u = hu + ku; (hk)u = h(ku).
[Simple example?]
(1996-09-30)

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