→ kerwinhui : 跟著提示做就可以了。Recall: Vandermonde det. 05/10 12:02
→ wayne0824 : 中間是A^2v 05/10 12:43
Suppose that A∈M_n(F) is a diagonalizable matrix with n distinct eigenvalues. Show that there exists a (column) vector v so that v,Av,A^v,...,A^n-1 v are linearly independent.
[Hint: Consider the sum of the eigenvectors.]
這題作業想了好久，請大家幫幫忙
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 223.139.244.230
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1462852351.A.A6A.html