能不能提供几个三阶幂零矩阵的例子？A为幂零矩阵 A^3=0

Question

A为幂零矩阵 A^3=0

Answer 1

A1 = O
A2 =
[0 0 1]
[0 0 0]
[0 0 0]
A3 =
[0 1 0]
[0 0 0]
[0 0 0]
A4 =
[0 0 0]
[0 0 1]
[0 0 0]
............................

Answer 2

A=0肯定算一个
0 1 0
0, 0, 0
0 , 0 ,0
也算一个
实际上任意diag(J1, J2, ..., Jn)都是，只要Ji是特征值为0的2阶Jordan标准型，或者是0矩阵