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