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Level 3
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.

Illustration Levi-Civita symbol: Cyclic (even) permutation of indices

Levi-Civita symbol: Cyclic (even) permutation of indices

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An even (cyclic) permutation of the indices \( \class{blue}{i} \), \( \class{red}{j} \), and \( \class{green}{k} \) of the Levi-Civita symbol \( \varepsilon_{\class{blue}{i}\class{red}{j}\class{green}{k}} \) results from rotating the indices clockwise (or counterclockwise) like this:\[ \varepsilon_{\class{blue}{i}\class{red}{j}\class{green}{k}} ~\rightarrow~ \varepsilon_{\class{green}{k}\class{blue}{i}\class{red}{j}} ~\rightarrow~ \varepsilon_{\class{red}{j}\class{green}{k}\class{blue}{i}} \]

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  • License: CC BY 4.0This illustration may be used with indication of the copyright!
  • Copyright: © 2021
  • This illustration was uploaded by FufaeV on .
  • This illustration was updated by FufaeV on .