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Lame matrix calculus question: Suppose you have that $y$ is an $n \times 1$ vector function of $t$ and $G$ is an $n \times n$ symmetric matrix function of $t$. Is it ok to write

$\frac{d}{dt}(y^T G y) = 2 \frac{d(y^T)}{dt} G y + y^T \frac{dG}{dt}y$,

where superscript $T$ denotes the transpose?

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    Use $\frac{d}{dt}(y^T G y) =(\frac{dy^T}{dt} G y)+(y^T \frac{dG}{dt} y)+(y^T G \frac{dy}{dt})$. So if $(\frac{dy^T}{dt} G y)=(y^T G \frac{dy}{dt})$ your result is correct. But maybe you already know and I missed something...2012-07-19
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    Yes, this is what I thought. I am just trying to make sure I didn't cock up because if not the rest of my proof would be wrong. Thanks...2012-07-19
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    Where does $G$ live? Is it symmetric? What about the $y$? Is it real?2012-07-19

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