diagonalizable linear map

可对角化线性映射

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

Translation evidence: Literature usage

Meaning in context

A finite-dimensional endomorphism possessing a basis of eigenvectors over the specified scalar field.

在指定标量域上具有一组特征向量基的有限维线性自映射。

Example

(2103)\begin{pmatrix}2&1\\0&3\end{pmatrix} is diagonalizable over Q\mathbb Q.

Usage and distinctions

A split characteristic polynomial does not suffice; a nontrivial Jordan block fails.

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Definition sources

  1. Wen-Wei Li — Elementary Algebra lecture notes, author manuscript§7.1 特征值与特征向量, Definition 7.1.3 (可对角化线性变换和矩阵), eigenvector-basis clause, 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 7.1.3 (可对角化线性变换和矩阵), eigenvector-basis clause, printed p.286 / PDF p.296 · Checked 2026-10-15
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