From 561bac75579391c14e47eaccfabdf9eda98855da Mon Sep 17 00:00:00 2001
From: Thomas Albers <thomas@thomaslabs.org>
Date: Wed, 27 Jul 2022 18:13:20 +0200
Subject: Initial commit

---
 math/levi_cevita.org | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)
 create mode 100644 math/levi_cevita.org

(limited to 'math/levi_cevita.org')

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*}
-- 
cgit v1.2.3