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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 again. I incorrectly copied the letters from my notebook. Is that better?2011-08-26

1 Answers 1

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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 $F^{\top}$.