vector space

向量空间

Algebra & Algebraic Geometry · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

An abelian group $V$ with a unital scalar action of a field $F$, distributive in both inputs and satisfying $(ab)v=a(bv)$.

配备域 $F$ 的标量作用的交换群，该作用保持两种加法、满足乘法结合律且 $1v=v$。

Example

$\mathbb C$ has real basis $1,i$.

Usage and distinctions

Dimension changes when the scalar field changes; specify that field.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source向量空间 (sec:vector-space), definition of 向量空间 and following field/left-right convention; module axioms in 基本概念 · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件向量空间 (sec:vector-space), definition of 向量空间 and following field/left-right convention; module axioms in 基本概念 · Checked 2026-10-15

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.