Re: [理工] [線代] 100台大資工
※ 引述《AM101 (新手)》之銘言：
: http://exam.lib.ntu.edu.tw/sites/default/files/exam/graduate/100/100419.pdf
: 第十題
: 不知道怎麼解...
: 請教一下解法
: 謝謝!
題目表示u和v長度相等且皆不為0
假設A(u,v) = T 為一個Orthogonal Matrix,
則T滿足 T^HT = I
若要滿足Tu=v, 則可把此T想成是householder matrix, 把u和經過u和v之平分線做鏡射,
就會得到v
(也可以想成是rotation matrix, 只是會做不到他要求的用u和v表示T)
所以此平分線之法向量w=u-v
→T=I-2*(w*w^H)/(w^H*w)
→A(u,v)=I-2*((u-v)*(u-v)^H)/((u-v)^H*(u-v)) 即為所求
EDIT: 有個地方打錯更正.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 119.14.22.116
※ 編輯: Jerrynet 來自: 119.14.22.116 (01/23 20:03)
推
01/23 20:59, , 1F
01/23 20:59, 1F
→
01/23 21:01, , 2F
01/23 21:01, 2F
推
01/23 21:02, , 3F
01/23 21:02, 3F
→
01/23 21:50, , 4F
01/23 21:50, 4F
→
01/23 22:05, , 5F
01/23 22:05, 5F
※ 編輯: Jerrynet 來自: 119.14.22.116 (01/23 22:19)
推
01/23 22:25, , 6F
01/23 22:25, 6F
→
01/23 22:25, , 7F
01/23 22:25, 7F
推
01/23 22:40, , 8F
01/23 22:40, 8F
→
01/23 22:41, , 9F
01/23 22:41, 9F
→
01/23 22:42, , 10F
01/23 22:42, 10F
推
01/24 00:02, , 11F
01/24 00:02, 11F
推
01/24 00:05, , 12F
01/24 00:05, 12F
→
01/24 00:06, , 13F
01/24 00:06, 13F
→
01/24 00:07, , 14F
01/24 00:07, 14F
→
01/24 00:07, , 15F
01/24 00:07, 15F
→
01/24 00:08, , 16F
01/24 00:08, 16F
推
01/24 00:14, , 17F
01/24 00:14, 17F
→
01/24 00:15, , 18F
01/24 00:15, 18F
→
01/24 00:16, , 19F
01/24 00:16, 19F
→
01/24 00:53, , 20F
01/24 00:53, 20F
推
01/24 00:54, , 21F
01/24 00:54, 21F
推
01/24 13:23, , 22F
01/24 13:23, 22F
推
01/24 19:28, , 23F
01/24 19:28, 23F
推
01/25 10:44, , 24F
01/25 10:44, 24F
→
09/11 14:48, , 25F
09/11 14:48, 25F
討論串 (同標題文章)