rank of a linear map

线性映射的秩

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

Translation evidence: Literature usage

Meaning in context

The dimension of the image of a linear map, measured over its scalar field.

线性映射的像作为标量域上的向量空间的维数。

Example

$(x,y)\mapsto(x,0)$ has rank one.

Usage and distinctions

Rank concerns the image; nullity concerns the kernel.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Xiamen University — Higher Algebra course team, lecture notes (2008)§4.4 线性映射的像与核, Definition 1, rank defined as dim Im φ, PDF p.1 · Checked 2026-10-15

Translation sources

1. 厦门大学数学科学学院 — 高等代数教案（08版）§4.4 线性映射的像与核, 定义1, dim Im φ 称为 φ 的秩, PDF p.1 · Checked 2026-10-15

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