作者christensen ()
看板Grad-ProbAsk
標題[問題] 線代的正交投影求解...
時間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
請問這題要怎麼求解呢? 麻煩順便告訴我計算過程吧~拜託了!
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1F：推 ssccg:設N(A^t)=span(2,-3,1)，得到一個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:另一個作法是取法向量w=(2,-3,1)，投影矩陣= I-(1/w^tw)ww^t 03/19 21:21
4F：推 s987692:正解～超強! 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