vector space

American  

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.

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vector space British  

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

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vector space Scientific  

1. 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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Etymology

Origin of vector space

First recorded in 1940–45

Example Sentences

Plotting words in a “vector space” makes it possible for an LLM to detect the connections among them: Distance is an easily computable property in a vector space, and closeness encapsulates relationships.

From The Wall Street Journal • Oct. 9, 2025

Let us traverse vector space hand-in-hand with our machines.

From The Wall Street Journal • Oct. 9, 2025

The corresponding transformations in this case are called linear transformations, and each must have a specified source and target vector space indicating which kinds of vectors arise as inputs and outputs.

From Scientific American • Sep. 14, 2021

Formally in mathematics, a vector is an element of something called a vector space.

From Forbes • Mar. 26, 2015