dimension of a vector space

向量空间的维数

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

Translation evidence: Literature usage

Meaning in context

The cardinality of any basis of a vector space over its specified field.

在指定标量域上，向量空间任一基的元素个数。

Example

dim⁡RC=2\dim_{\mathbb R}\mathbb C=2, while dim⁡CC=1\dim_{\mathbb C}\mathbb C=1.

Usage and distinctions

Infinite dimension is a cardinal, not a largest finite independent-set size.

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 def:dimension-vector-space (维数的不变性), cardinality of a basis · 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 def:dimension-vector-space (维数的不变性), cardinality of a basis · Checked 2026-10-15
Edit source / propose a PRReport a correction

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