[線代] 有關特徵向量 證明線性獨立

看板Math作者 (萊恩)時間9年前 (2016/05/10 11:52), 編輯推噓0(002)
留言2則, 2人參與, 最新討論串1/1
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

05/10 12:02, , 1F
跟著提示做就可以了。Recall: Vandermonde det.
05/10 12:02, 1F

05/10 12:43, , 2F
中間是A^2v
05/10 12:43, 2F
文章代碼(AID): #1NCLh_fg (Math)