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I'm trying to manipulate a matrix equation I've got. Here's what it looks like:

$R_\mathrm{app} = U \cdot F^T$

where $R_\mathrm{app}, U, F$ are matrices. $R_\mathrm{app}$ is a size of $u \times a$, $U$ is the size of $u \times f$ and $F$ if the size of $a \times f$

For the context of the problem please read chapter II of http://classes.soe.ucsc.edu/cmps242/Winter08/proj/serdar_report.pdf. The main part is the last paragraph of chapter II.

So I'd like to get an equation for U out if this. How do I need to manipulate this equation to get U on one side and the other two on the other side.

If you could include the procedure of the manipulation, it would be much appreciated.

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I edited the question. Is that what you needed? –  gligoran Aug 26 '11 at 13:50
    
I edited again. I incorrectly copied the letters from my notebook. Is that better? –  gligoran Aug 26 '11 at 13:56
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1 Answer

up vote 3 down vote accepted

If the dimensions work out the try this:

$$ R_{\rm app} = U \cdot F^{\top} $$

$$ R_{\rm app}\cdot F = U \cdot (F^{\top}\cdot F) $$

$$ R_{\rm app} \cdot F \cdot ( F^{\top} \cdot F)^{-1} = U $$

where $F \cdot ( F^{\top} \cdot F)^{-1}$ is the pseudo inverse of $F^{\top}$.

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