characteristic polynomial of a linear map

线性映射的特征多项式

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

Translation evidence: Literature usage

Meaning in context

For an endomorphism of an $n$-dimensional $F$-space, the basis-independent monic polynomial $\det(xI-A)$.

有限维线性自映射在任一基下的矩阵 $A$ 所给出的首一多项式 $\det(xI-A)$。

Example

For $A=\operatorname{diag}(2,3)$ it is $(x-2)(x-3)$.

Usage and distinctions

Some sources use $\det(A-xI)$; it differs by $(-1)^n$ from the monic convention here.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Elementary Algebra lecture notes, author manuscript§5.8 特征多项式和 Cayley–Hamilton 定理, Definition 5.8.2 and Proposition 5.8.3 with following basis-independence paragraph, printed pp.213–214 / PDF pp.223–224 · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学讲义，作者公开稿§5.8 特征多项式和 Cayley–Hamilton 定理, Definition 5.8.2 and Proposition 5.8.3 with following basis-independence paragraph, printed pp.213–214 / PDF pp.223–224 · Checked 2026-10-15

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