In the link http://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudoinverse, it talks about solving $Ax=b$ by $x = A^+b + [I − A^+A]w$ for any vector $w$. Let's say $A$ is $m\times n$, and $b$ and $x\in \mathbb{R}^n$. My question is: since $w$'s $n$ components are in general more than needed given the kernel of $A$ might be of dimension $n-r\gt 0$, how to use Moore–Penrose pseudoinverse $A^+$ to give an explicit solution with the least number of free parameters?
a question regarding the use of Moore–Penrose pseudoinverse
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linear-algebra
matrices
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0This link might be helpful to you. It shows you how to use Moore-Penrose pseudoinverse in MATLAB and also gives an neat example. http://www.mathworks.com/help/techdoc/ref/pinv.html – 2011-02-15
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0@Sunil: unfortunately, the link does not help. :( – 2011-02-15