作者christensen ()
看板Grad-ProbAsk
标题[问题] 线代的正交投影求解...
时间Thu Mar 19 21:00:07 2009
Determine a transformation matrix that can orthogonally project any
vector (for example, the vector(3,4,5)) onto the plane of 2x - 3y + z = 0
请问这题要怎麽求解呢? 麻烦顺便告诉我计算过程吧~拜托了!
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 118.170.99.106
1F：推 ssccg:设N(A^t)=span(2,-3,1)，得到一个A=[(1 0 -2)^t (0 1 3)^t] 03/19 21:18
2F：→ ssccg:然後用公式，投影到R(A)的matrix = A(A^tA)^-1 A^t 03/19 21:19
3F：→ ssccg:另一个作法是取法向量w=(2,-3,1)，投影矩阵= I-(1/w^tw)ww^t 03/19 21:21
4F：推 s987692:正解～超强! 03/19 22:20
5F：推 hatacpk:把(3,4,5)扣掉(3,4,5)投影在(2,-3,1)就是答案了 03/20 20:42