basis of a vector space

向量空间的基

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

Translation evidence: Literature usage

Meaning in context

A linearly independent family spanning the vector space by finite linear combinations.

通过有限线性组合生成整个向量空间的线性无关向量族。

Example

$1,x,x^2$ is a basis of $F[x]_{\le2}$.

Usage and distinctions

A spanning family can have redundancy; a basis cannot.

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-theorem naming 基, items (i)–(iv), in particular unique finite expansions; specialize D to a field · 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-theorem naming 基, items (i)–(iv), in particular unique finite expansions; specialize D to a field · Checked 2026-10-15

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