设A为你三方阵,a1,a2为A的分别属于特征值-1,1的特征向量,向量a3满足Aa3=a2+a3,令P=(a1,a2,a

由已知
AP = A(a1,a2,a3)
= (Aa1,Aa2,Aa3)
= (-a1,a2,a2+a3)
= (a1,a2,a3) B
B=
-1 0 0
0 1 1
0 0 1
所以 AP = PB
所以 P^-1AP = B =
-1 0 0
0 1 1
0 0 1