How do I solve for column vector from a matrix

2014 3 6
1 个回答
更新时间：2014 3 7
2 次查看（30 天）

0 个投票

Hello,
I want to find column matrix [a1 a2]'
[a1 a2]'*[a1 a2] = [1 0; 1 0];
how do I do that?
thanks

5 个评论
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Matt J
Matt J 2014-3-6
There is no solution to the equation you've shown. The left hand side is a symmetric matrix. The right hand side is not.
Suma
Suma 2014-3-6
for example, take a1=1, a2=0
[1 0]'*[1 0] = [1 0; 0 0]
But the matrix(RHS) could be anything, isn't it possible to solve this?
Matt J
Matt J 2014-3-6
编辑：Matt J 2014-3-6
But the matrix(RHS) could be anything, isn't it possible to solve this?
Nope.
Suma
Suma 2014-3-6
notice that [a1 a2]' is a column vector and [a1 a2] a row vector which are being multiplied
Matt J
Matt J 2014-3-6
编辑：Matt J 2014-3-6
Yep. In addition to being symmetric, the left hand side expression is also rank 1. That means the right hand side would at least have to have those same properties.

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回答（1 个）

Jos (10584)
Jos (10584) 2014-3-7

1 个投票

(1) [a ; b] * [a b] = [a*a a*b ; b*a b*b] % by definition
(2) [a ; b] * [a b] = [1 0 ; 1 0] % by request
=> b*b = 0 => b is 0
b*a = 1 => b is not 0
Impossible!

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Suma
Suma
2014-3-6

回答：

Jos (10584)
Jos (10584)
2014-3-7

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