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author | Thomas Albers <thomas@thomaslabs.org> | 2023-03-08 23:43:00 +0100 |
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committer | Thomas Albers <thomas@thomaslabs.org> | 2023-03-08 23:43:00 +0100 |
commit | 61b5ce20f25c5785e41574998a12c6d06eb05a5e (patch) | |
tree | 20e2225b4f30b15d8dee30351041d1f33d42b34a /math/levi_cevita.org | |
parent | 561bac75579391c14e47eaccfabdf9eda98855da (diff) |
Diffstat (limited to 'math/levi_cevita.org')
-rw-r--r-- | math/levi_cevita.org | 26 |
1 files changed, 0 insertions, 26 deletions
diff --git a/math/levi_cevita.org b/math/levi_cevita.org deleted file mode 100644 index aaa2074..0000000 --- a/math/levi_cevita.org +++ /dev/null @@ -1,26 +0,0 @@ -#+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*} |