[線代] orthogonal projection

看板Math作者 (無法顯示)時間14年前 (2011/09/08 21:38), 編輯推噓1(1推 0噓 8→)
留言9則, 1人參與, 最新討論串1/2 (看更多)
1. If w is the orthogonal projection of a vector v in R^n onto a subspace W of R^n then w is orthogonal to v False ======== 2. Let W be a subspace of R^n and v be a vector in R^n. Among all vectors in W, + the vector closet to v is the orthogonal projection of v onto W False ========= 3. The set of all vectors in R^n orthogonal to one fixed vector is a subspace of R^n True ================ + 4. If W is a subspace of R^n, then W and W have no vectors in common False ========= 5. If a square matrix has orthonormal columns, then it also has orthonormal rows True 請問這些是為甚麼呢? 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.166.113.145
推
09/08 21:45, , 1F
R^3 P(x,y,z)=(x,y,0) is a projection
09/08 21:45, 1F
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09/08 21:46, , 2F
(x,y,z)‧(x,y,0)≠0
09/08 21:46, 2F
→
09/08 21:47, , 3F
3. 就照定義證明Given u. Suppose W={v|v垂直u}
09/08 21:47, 3F
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09/08 21:47, , 4F
(av_1+bv_2)‧u=0
09/08 21:47, 4F
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09/08 21:48, , 5F
and 0屬於W
09/08 21:48, 5F
→
09/08 21:48, , 6F
4 0 in W and W┴
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09/08 21:49, , 7F
A^TA=I A^{-1}=A^T hence AA^T=I
09/08 21:49, 7F
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09/08 21:50, , 8F
上面是第五題
09/08 21:50, 8F
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09/08 21:50, , 9F
第二題最靠近的好像是project to W
09/08 21:50, 9F
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文章代碼(AID): #1EQCL5jW (Math)
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文章代碼(AID): #1EQCL5jW (Math)