linear map

线性映射

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

Translation evidence: Literature usage

Meaning in context

A map $T:V\to W$ between vector spaces over the same field $F$ satisfying $T(av+bw)=aT(v)+bT(w)$.

同一域上向量空间之间保持线性组合的映射。

Example

$D(a+bx+cx^2)=b+2cx$ is real-linear.

Usage and distinctions

Conjugation on $\mathbb C$ is real-linear but not complex-linear.

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Definition sources

1. Wen-Wei Li — Elementary Algebra lecture notes, author manuscript§4.5 线性映射, Definition 4.5.1 (线性映射), printed p.129 / PDF p.139 · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学讲义，作者公开稿§4.5 线性映射, Definition 4.5.1 (线性映射), printed p.129 / PDF p.139 · Checked 2026-10-15

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