Levi-Civita Symbol

$$\varepsilon_{ijk}=

\begin{cases}
-1,\quad \text{odd permutation of } \varepsilon_{ijk}\\\\~~~0,\quad \text{otherwise}
\end{cases}$$
* An even permutation means an even number of swaps between index positions
* $\displaystyle \varepsilon_{ijk}$ is $\displaystyle 0$ when any of $\displaystyle i,j,k$ are equal
## $\displaystyle \varepsilon_{ijk}\varepsilon_{imn}=\delta_{jm}\delta_{kn}-\delta_{jn}\delta_{km}$
* $\displaystyle \delta_{jm}$ is the [[Kronecker Delta]]
* From [Continuum Mechanics textbook](https://www.continuummechanics.org/tensornotationadvanced.html)````