特征值的代数重数定义

摘自 Linear Algebra and its applications David C. Lay Chapter 5.2, Page 276

特征值的几何重数定义

The geometric multiplicity of $c$ is the dimension of the eigenspace of $A$ associated with $c$.

摘自 The Linear Algebra a Beginning Graduate Student Ought to Know (Second Edition) Jonathan S. Golan
Chapter12, Page 244 ,有改动

semisimple eigenvalue 和 spectrum 定义

If these two multiplicities(geometric multiplicity & algebraic multiplicity) are equal, we say that $c$ is a semisimple eigenvalue of $A$

The set of all eigenvalues of $A$ is called the spectrum of $\alpha$ and is denoted by $spec(A)$

摘自 The Linear Algebra a Beginning Graduate Student Ought to Know (Second Edition) Jonathan S. Golan
Chapter12, Page 244 ,有改动

定理

注：

摘自 《矩阵论教程》——张绍飞 Page 23