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Eddington permutation symbol "e"

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Old   February 18, 2000, 05:51
Default Eddington permutation symbol "e"
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rajesh
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I recently came across the mathematical term "Eddington permutation" when trying to use tensor analysis to make a 3D grid around a ship surface. Could someone tell me what it means? Thank you, rajesh
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Old   February 18, 2000, 12:20
Default Re: Eddington permutation symbol "e"
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COBOK
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I believe you are talking about the permutation symbol e\ijk, that often is used to symbolically represent the cross product in indexial notations as AxB=e\ijkA\jB\k. (Note that I'm using \i to represent lower index). Also, A and B are vectors. Here, e\123=e\231=e\312=1 (positive permutation of indexes), e\132=e\213=e\321=-1 (negative permutation), otherwise e\ijk=0 (i.e. if any repeating combination of indexes occur).

Also, note that e\ijk is NOT a tensor, as it does not satisfy the tensor transformartion rule. However, many people used to call it "tensor".

It is a very useful symbol to make your notes elegant and compact.
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Old   February 19, 2000, 18:34
Default Re: Eddington permutation symbol "e"
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Jonas Larsson
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Yep, and he is probably confusing "Eddington" with "Einstein". The eps_ijk is sometimes called "Einstein's permutation symbol". Antother name for it is "Levi-Civita Tensor Density"
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Old   February 21, 2000, 00:18
Default Re: Eddington permutation symbol "e"
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rajesh
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Thank you so much guys.
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