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Diffstat (limited to 'math/levi_cevita.org')
| -rw-r--r-- | math/levi_cevita.org | 26 |
1 files changed, 26 insertions, 0 deletions
diff --git a/math/levi_cevita.org b/math/levi_cevita.org new file mode 100644 index 0000000..aaa2074 --- /dev/null +++ b/math/levi_cevita.org @@ -0,0 +1,26 @@ +#+TITLE: The Levi Cevita Symbol +#+SETUPFILE: ../math_options.org +#+LATEX_HEADER: \usepackage{bm} +#+LATEX_HEADER: \usepackage{mathtools} + +* Disclaimer +This site as of now just a technology demonstration and its claims +should not be taken as true (even though I myself am pretty confident +they are) +* Levi Cevita symbol +\begin{equation*} +\varepsilon_{ijk} = \left\{\begin{array}{rl} +1,&(i,j,k) \in \{(1,2,3), (2,3,1), (3,1,2)\}\\ +-1,&(i,j,k) \in \{(3,2,1), (2,1,3), (1,3,2)\}\\ +0,&\text{otherwise} +\right{} +\end{array} +\end{equation*} + +\begin{equation*} +\varepsilon_{ijk} = \varepsilon_{jki} = \varepsilon_{kij} = - \varepsilon_{ikj} = - \varepsilon_{jik} = - \varepsilon_{kji} = 1 +\end{equation*} + +\begin{align*} +\sum_{k=1}^3 \varepsilon_{ijk}\varepsilon_{kmn} = \delta_{im} \delta_{jn} - \delta_{in} \delta_{jm} +\end{align*} |