作者wakke (合理化勒索)
看板Math
标题[线代] 证明题
时间Thu Jul 14 10:14:15 2011
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
似乎有在教科书出现过，不过还是不会..
希望有人能解迷津或给个答题的方向，
感谢感谢。
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1F：→ LiamIssac :eigenvalue? 07/14 13:51
2F：推 zyjheng :consider minimal polynomial, since over R, 07/14 13:53
3F：→ zyjheng :1 should be an eigenvalue. 07/14 13:53