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Benedict Irwin edited Sketchy Generation.tex
over 9 years ago
Commit id: b893a852372a664c36330f188b161bebb7d899e0
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\end{equation}
The first operation takes a vector and generates a skew symmetric matrix. The third operation defines the Levi-Civita symbol, a rank $3$ tensor which is essential to vector
calculus. calculus and higher dimensional generalisations. A use of the first operation would be to define the electromagnetic tensor which looks like \begin{equation}
F_{\mu\nu}=\begin{bmatrix} 0 & E_x/c & E_y/c & E_z/c \\ -E_x/c & 0 & B_z & -B_y \\ -E_y/c & -B_z & 0 & B_x \\ -E_z/c & B_y & -B_x & 0 \end{bmatrix}
\end{equation}