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.

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

vector space

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).

Word History and Origins

Origin of vector space¹

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.

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If it read enough poetry, eventually it would figure out that “sweet” and “sour” have related meanings—that their vectors are both in the “taste” cluster in vector space—while “because” and “fermented” do not.

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

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When they plotted the phase in an abstract “wave vector space” — something that’s done in quantum physics all the time, but not often in earth science — they saw that the phase spiraled around and formed a vortex: The twisting in the waves’ phases resembled the spiraling wave functions in a topological insulator.

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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.

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