[線代] projection matrix

看板Math作者 (無法顯示)時間14年前 (2011/06/11 20:03), 編輯推噓1(1推 0噓 4→)
留言5則, 3人參與, 最新討論串1/1
if P_3*3 is a projection matrix that projects any vector in R^3 onto the vector u=[1 1 1]^T, then there must be two eigenvectors that correspond to the eigenvalue of 0 書上寫ture 請問為什麼呢? 謝謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.166.116.20
→
06/11 20:26, , 1F
我的想法有點笨，把P求出來再檢查
06/11 20:26, 1F
→
06/11 20:26, , 2F
P = A(A^T A)^(-1) A^T
06/11 20:26, 2F
推
06/11 22:11, , 3F
R3中至少有兩個不平行的向量跟(1 1 1)^T垂直
06/11 22:11, 3F
→
06/12 02:06, , 4F
rank(P) = 1, 故 nullity(P)=2.
06/12 02:06, 4F
→
06/12 02:07, , 5F
P 不一定是垂直投影矩陣.
06/12 02:07, 5F
‣ 更多 mqazz1 的文章
文章代碼(AID): #1DyrcRUJ (Math)