Question

这个矩阵的n次幂怎么求?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