Question

这个矩阵的n次幂怎么求?谢谢

A= 1 -√3
√3 1
求这个矩阵的n次幂

Answer 1

A^2 =
-2 -2√3
2√3 2

A^3 = AA^2 =
-8 0
0 -8
= -8E.

所以
当n = 3k 时, A^n = (A^3)^k = (-8E)^k = (-8)^kE
当n = 3k+1 时, A^n = A(A^3)^k = A(-8E)^k = (-8)^kA
当n = 3k+2 时, A^n = A^2(A^3)^k = A^2(-8E)^k = (-8)^kA^2 = (-8)^k *
-2 -2√3
2√3 2

Answer 2

1 ，(-1)^n*3^(n/2)
3^(n/2),1