有幾題觀念想請教一下
第6題
Which of the following statements are true?
選項(B)
The shortest (minimal 2-norm) least-squares solution to a problem Ax=b
must be in the row space of A
這個選項答案給對
我知道least squares solution 也知道minimal 2-norm solution
那他合在一起是指什麼意思，如果是指minimal solution不是應該在R(A^T)內嗎?
還是R(A^T) = row space of A ?? 觀念不太好不好意思
另外第8題 [2 3 1 5]
Given a matrix A = [2 3 0 4], which of the following statements are TRUE?
[0 0 1 1]
選項(E)
If the two systems Ax=b and Ax=c have the same shortest(minimal 2- norm)
least squares solution, then the projections of b and c onto the column
space of A must be identical.
請問為什麼這個選項也對?
謝謝

第6題:思考矩陣轉置...A^T的Range(或說CS)不就是沒轉置前的RS(A)嗎?第8題:b,c minimal solution相同,令此解為s,那b,c對CS(A)的投影是As,故極小解相同時投影也相同你這樣講也正確唷 , 就只是依照定義展開會是一樣的線性組合