Benedict Irwin edited Sketchy Generation.tex  over 9 years ago

Commit id: b7d2cad0ff9fcd881d0ddb1565a2f723522c78d8

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=\epsilon^{klm}\partial_lF_m\hat{\mathbf{e}}_k  \end{equation}  One could seek to create another operator (that maps f(x,y,z)) to a vector of the form \begin{equation}  \hat{O}=  \begin{vmatrix}  \textbf{i} & \textbf{j} & \textbf{k} \\  \partial_x & \partial_y & \partial_z \\  \partial_x & \partial_y & \partial_z   \end{vmatrix}  =\textbf{i}(\partial_y\partial_z-\partial_z\partial_y)-...  \end{equation}  But the laws of partial derivatives being commutative forbid this mapping to any vecotr other than (0,0,0)...