λ=0 是矩陣的特征值,A =
[1 0 1]
[0 2 0]
[1 0 a]
detA = 2(a-1)=0,則 a=1.
|λE-A| =
|λ-1 0 -1|
|0 λ-2 0|
|-1 0 λ-1|
|λE-A| =(λ-2)[(λ-1)^1-1]= λ(λ-2)^2,
得 特征值 λ=0,2,2.
對于 λ=0,λE-A =
[-1 0 -1]
[0 -2 0]
[-1 0 -1]
行初等變換為
[1 0 1]
[0 1 0]
[0 0 0]
特征向量是 (1,0,-1)^T;
對于重特征值 λ=2,λE-A =
[1 0 -1]
[0 0 0]
[-1 0 1]
行初等變換為
[1 0 -1]
[0 0 0]
[0 0 0]
特征向量是 (1,0,1)^T,(0,1,0)^T.