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Benedict Irwin edited Sketchy Generation.tex
over 9 years ago
Commit id: 0cb72d8d813d669db3510812b5b6f9799172455f
deletions | additions
diff --git a/Sketchy Generation.tex b/Sketchy Generation.tex
index 6935d28..beac4d4 100644
--- a/Sketchy Generation.tex
+++ b/Sketchy Generation.tex
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\partial_x\partial_y & \partial_y^2 & \partial_z\partial_y \\
\partial_x\partial_z & \partial_y\partial_z & \partial_z^2
\end{bmatrix}
\end{equation}
As the divergence operator maps a vecotr field to a scalar field it must be a row vector. As the divergence of any curl is zero it must result in 0 under the left operation. This gives a likely form \begin{equation}
\begin{bmatrix} \partial_z^{-1}\partial_y^{-1} & \partial_z^{-1}\partial_x^{-1} & \partial_y^{-1}\partial_x^{-1} \end{bmatrix}
\begin{bmatrix}
0 & -\partial_z & \partial_y \\
\partial_z & 0 & -\partial_x \\
-\partial_y & \partial_x & 0
\end{bmatrix}
=\begin{bmatrix}1-1&1-1&1-1\end{bmatrix}
\end{equation}