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 c c is the dimension of the eigenspace of A A A associated with c c 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 c c is a semisimple eigenvalue of A A A

The set of all eigenvalues of A A A is called the spectrum of α \alpha α and is denoted by s p e c ( A ) \mathit{spec(A)} 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