Re: [線代] Householder
※ 引述《handsomepow (handsomepow)》之銘言:
: 1.Let x = (1,0,4,6,3,4)^T. Find a Householder transformation H
: and a positive number α such that Hx = (1,α,4,6,0,0)^T
Lemma:
n*1 x-y
Suppose x,y in |R, ||x||=||y||. Let u=-------, and H be the Householder
2 T ||x-y||
matrix, then (1)||x-y|| =2(x-y)x
(2) Hx=y
證明就硬幹就好了XDDD
一個簡單的推廣
T n*1
Let x=[x ... x ] in |R . If α=||x|| and y=αe , then the Householder
1 n 1
x-y
matrix H of u= ------- transfer x to y. i.e. H(x)=αe_1
||x-y||
所以用這樣的方式可以讓 [0 3 4] 變成 [α 0 0],把這個矩陣叫做H'
要保長度所以可以知道 α=5
你算這個之後得到的H'長[0 0.6 0.8 ]
[0.6 0.64 -0.48]
[0.8 -0.48 0.36]
填進去最後的H要照column填入
得到[1 0 0 0 0 0 ]
[0 0 0 0 0.6 0.8 ]
[0 0 1 0 0 0 ]
[0 0 0 1 0 0 ]
[0 0.6 0 0 -0.64 0.48]
[0 0.8 0 0 -0.48 0.36]
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 111.251.138.227
→
11/22 23:54, , 1F
11/22 23:54, 1F
→
11/22 23:56, , 2F
11/22 23:56, 2F
推
11/23 08:48, , 3F
11/23 08:48, 3F
→
11/23 09:03, , 4F
11/23 09:03, 4F
→
11/23 10:49, , 5F
11/23 10:49, 5F
不過因為alpha在中間所以我要想一下要怎麼換
線代頭腦不好拍謝QQ
※ 編輯: jacky7987 來自: 111.251.149.13 (11/23 11:19)
※ 編輯: jacky7987 來自: 111.251.149.13 (11/23 11:20)
※ 編輯: jacky7987 來自: 111.251.149.13 (11/23 11:20)
推
11/23 18:31, , 6F
11/23 18:31, 6F
感謝
※ 編輯: jacky7987 來自: 111.251.152.225 (11/23 18:55)
→
11/23 19:01, , 7F
11/23 19:01, 7F
推
12/01 15:26, , 8F
12/01 15:26, 8F
討論串 (同標題文章)