eigenvalue of a linear map

线性映射的特征值

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

Translation evidence: Literature usage

Meaning in context

A scalar $\lambda\in F$ for which an endomorphism $T$ has a nonzero vector $v$ with $Tv=\lambda v$.

使线性自映射满足 $Tv=\lambda v$ 且存在非零 $v$ 的标量。

Example

$\operatorname{diag}(2,3)$ has eigenvalues $2,3$.

Usage and distinctions

The zero vector is never an eigenvector; eigenvalues must belong to the specified field.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Elementary Algebra lecture notes, author manuscript§7.1 特征值与特征向量, Definition 7.1.2 (特征值和特征向量), printed p.286 / PDF p.296 · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学讲义，作者公开稿§7.1 特征值与特征向量, Definition 7.1.2 (特征值和特征向量), printed p.286 / PDF p.296 · Checked 2026-10-15

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