Re: [矩陣] 請教二個矩陣問題
※ 引述《koei888 (^^)》之銘言：
: 1.令 A=(1-alph)I-alph*i*i^t 其中, 1>alph>0 求特性根、特性向量及逆矩陣
: A是 (n*n) 矩陣， i是單位向量 i^t 轉置單位向量
這題竟然都沒人回...
a = alph
考慮Q = [i q2 q3 ... qn] is an orthogonal matrix
we see that Ai = (1-2a)i and Aq = (1-a)q
so the eigenvalues of A are {1-2a, 1-a (multiplicities = n-1)}
if a is different from 1/2, then A is invertible
since A = Q * diag{1-2a, 1-a, ..., 1-a} * Q^T
so A^{-1} = Q * diag{1/(1-2a), 1/(1-a), ..., 1/(1-a)} * Q^T
= [1/(1-a)]I + [1/(1-2a) - 1/(1-a)] i*i^T
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 97.99.68.240
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1490754409.A.FF5.html
※ 編輯: cuttlefish (97.99.68.240), 03/29/2017 11:51:27
→
03/29 12:46, , 1F
03/29 12:46, 1F
→
03/30 00:13, , 2F
03/30 00:13, 2F
→
03/31 12:12, , 3F
03/31 12:12, 3F
討論串 (同標題文章)