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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.

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 vector See also scalar multiplication

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).

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## Word History and Origins

Origin of vector space^{1}

First recorded in 1940–45

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