推 gensim:P=(U^-1)V 變成B2->B1...... 09/10 23:57
→ gogogoclark:P為B2->B1的座標轉換矩陣也可為B1->B2的基底轉換矩陣 09/11 00:48
推 gensim:....有可以這樣亂轉的嗎... 09/12 00:06
※ 引述《nowar100 (拋磚引玉)》之銘言：
: 題目：
: n
: Let A1 be the matrix representation of a linear transformation L from R to
: n n
: R with respect to the basis B1. Let B2 be another basis of R , and let P be
: the transition matrix corresponding to the change of basis from B1 to B2,
: What is the matrix representation of L with respect to the basis B2 ?
: 我的想法：
: B2 B1 -1
: [L] = [I] [L] [I] = P A1 P
: B2 B1 B1 B2
: -1
: 可是解答是 P A1 P ，我不懂我錯在哪，麻煩大家了
令U為B1的基底, V為B2的基底
令U為B1的基底, V為B2的基底
-1
x= U x =V x => x = U V x
B1 B2 B1 B2
-1
令P=U V => U P= V P為B1->B2的基底轉換矩陣
-1
L(x)=y L U x =U y => U L U x = y
B1 B1 B1 B1
-1 -1
=> U L U= [L] = A1 同理 V L V= [L]
B1 B2
-1 -1
=> L= U [L] U = V [L] V
B1 B2
-1 -1 -1 -1
=> [L] =V U [L] U V = P [L] P =P A1 P
B2 B1 B1
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 123.192.99.249