# 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 of vector space
1940-1945
1940-45
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
Cite This Source
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
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
Cite This Source
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
Cite This Source
vector space in Technology

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)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
Cite This Source

### Difficulty index for vector space

Few English speakers likely know this word

### Word Value for vector

11
13
Scrabble Words With Friends