[理工] [线代]102交大资联

楼主: hyc1227   2015-01-10 10:32:05
有几题观念想请教一下
第6题
Which of the following statements are true?
选项(B)
The shortest (minimal 2-norm) least-squares solution to a problem Ax=b
must be in the row space of A
这个选项答案给对
我知道least squares solution 也知道minimal 2-norm solution
那他合在一起是指什么意思,如果是指minimal solution不是应该在R(A^T)内吗?
还是R(A^T) = row space of A ?? 观念不太好不好意思
另外第8题 [2 3 1 5]
Given a matrix A = [2 3 0 4], which of the following statements are TRUE?
[0 0 1 1]
选项(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.
请问为什么这个选项也对?
谢谢
作者: qoojordon (颖川琦)   2015-01-10 11:45:00
第6题:思考矩阵转置...A^T的Range(或说CS)不就是没转置前的RS(A)吗?第8题:b,c minimal solution相同,令此解为s,那b,c对CS(A)的投影是As,故极小解相同时投影也相同你这样讲也正确唷 , 就只是依照定义展开会是一样的线性组合

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