English Dictionary

vector space

名詞

(algebra, geometry, mathematics, topology) A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints.

日本語の意味

数学において、ベクトルと呼ばれる要素の集合に対し、加法やスカラー倍などの演算が定義され、各種の線形性（例：分配律や結合律）や零ベクトルの存在などの条件を満たす代数的構造（線形空間）を指す。

During the lecture, the professor showed how a vector space can be constructed from polynomial functions of degree at most n.

講義で教授は、次数が高々nの多項式から、加法とスカラー倍の演算（標準的な公理を満たす）を備えた体上のベクトルの集合としてのベクトル空間がどのように構成されるかを示した。

意味（1）

(algebra, geometry, mathematics, topology) A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints.

A vector space is a set of vectors which can be linearly combined.

vector spaces （ plural ）