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Consider matrices $Y\in\mathbb{R}^{n\times n}$ and $X\in\mathbb{R}^{n\times m}$ where $m\geq n$. $X$ is unknown but $Y=XX'$, which implies that $Y$ is positive definite (I see no reason why this couldn't alternately be expressed as a positive semi-definite problem with $Y=X'X$, a different $Y\in\mathbb{R}^{m\times m}$ would still be known).

What the easiest method to find $X$? I was thinking of minimizing the Frobenius norm, but wasn't sure if there was some relatively straightforward thing that I'm missing.

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    Notice the typographical difference between $Y\epsilon\mathbb{R}^{n\times n}$ and $Y\in\mathbb{R}^{n\times n}$. Writing \in rather than \epsilon not only makes the symbol look different, but also results in proper spacing, since those conventions are built in to the software. $\TeX$ is fairly sophisticated. (I changed it in the posting.)2012-09-11
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    When I see epsilon, I think of [Hilbert choice operator](http://en.wikipedia.org/wiki/Epsilon_calculus#Hilbert_notation), but of course the [arity](http://en.wikipedia.org/wiki/Arity) is different..2012-09-11
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    @MichaelHardy Thanks.2012-09-12

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