[線代] 證明題

[wakke (合理化勒索)]

Let A be an n*n matrix over R such that A^5=I .Here, as usual,

I denotes the identity matrix.

Show that if the trace tr(A)=0 , then  Av=v  holds,

for some non-zero vector v

似乎有在教科書出現過，不過還是不會..

希望有人能解迷津或給個答題的方向，

感謝感謝。

--

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 218.166.112.125
→ LiamIssac   :eigenvalue?
推 zyjheng     :consider minimal polynomial, since over R,
→ zyjheng     :1 should be an eigenvalue.