[線代] 正交矩陣必可對角化?
如題
我在寫考古題時
解答突然說了這句
也沒解釋,就繼續做下去了
**
不好意思,我把問題敘述的更清楚點
我想問,不論是佈於C或R,
特徵根如果皆不相同當然可以對角化
那如果是1,1,-1 或1,1,1
這樣是不是要討論幾何重數和代數重數必相等?
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 111.253.19.26
→
01/20 16:41, , 1F
01/20 16:41, 1F
推
01/20 16:59, , 2F
01/20 16:59, 2F
→
01/20 17:03, , 3F
01/20 17:03, 3F
喔 對阿 我也在想是over R or over C ,題目是
A 3 by 3 real matrix T is said to be in SO(R,3) if det(T)=1 and ||Tx||=||x||
^^^^^^^
for all x 屬於 R^3. 其實這裡我看不懂
(1)show that for such T there is a nontrivial u 屬於 R^3 such that Tu=u.
(2)find the Jordan canonical form of each T.
解答都只有考慮λ=±1 ,我是覺得還要考慮如λ=1/√2±1/√2 i 吧
然後我是卡在第二題
※ 編輯: nobrother 來自: 111.253.19.26 (01/20 17:30)
→
01/20 17:46, , 4F
01/20 17:46, 4F
→
01/20 17:47, , 5F
01/20 17:47, 5F
→
01/20 18:01, , 6F
01/20 18:01, 6F
→
01/20 18:12, , 7F
01/20 18:12, 7F
→
01/20 18:13, , 8F
01/20 18:13, 8F
→
01/20 18:14, , 9F
01/20 18:14, 9F
→
01/20 18:15, , 10F
01/20 18:15, 10F
→
01/20 18:16, , 11F
01/20 18:16, 11F
→
01/20 19:06, , 12F
01/20 19:06, 12F
→
01/20 19:07, , 13F
01/20 19:07, 13F
→
01/20 19:44, , 14F
01/20 19:44, 14F
→
01/20 19:46, , 15F
01/20 19:46, 15F
→
01/20 19:46, , 16F
01/20 19:46, 16F
→
01/20 19:54, , 17F
01/20 19:54, 17F
→
01/20 19:56, , 18F
01/20 19:56, 18F
→
01/20 19:59, , 19F
01/20 19:59, 19F
→
01/20 20:00, , 20F
01/20 20:00, 20F
※ 編輯: nobrother 來自: 111.253.19.26 (01/21 00:33)
→
01/21 01:23, , 21F
01/21 01:23, 21F
→
01/21 01:24, , 22F
01/21 01:24, 22F
→
01/21 01:25, , 23F
01/21 01:25, 23F
→
01/21 01:25, , 24F
01/21 01:25, 24F
→
01/21 01:25, , 25F
01/21 01:25, 25F
→
01/21 10:24, , 26F
01/21 10:24, 26F
→
01/21 10:24, , 27F
01/21 10:24, 27F
→
01/21 16:09, , 28F
01/21 16:09, 28F
→
01/21 16:09, , 29F
01/21 16:09, 29F
→
01/21 19:30, , 30F
01/21 19:30, 30F
推
01/22 10:50, , 31F
01/22 10:50, 31F
→
01/22 13:50, , 32F
01/22 13:50, 32F
→
01/02 15:39,
7年前
, 33F
01/02 15:39, 33F
→
07/07 11:49,
6年前
, 34F
07/07 11:49, 34F