# [Numpy-discussion] permutation symbol

Charles R Harris charlesr.harris@gmail....
Tue Jun 30 11:27:05 CDT 2009

On Tue, Jun 30, 2009 at 5:11 AM, Nils Wagner
<nwagner@iam.uni-stuttgart.de>wrote:

> On Tue, 30 Jun 2009 11:22:34 +0200
>  "Nils Wagner" <nwagner@iam.uni-stuttgart.de> wrote:
>
>>  Hi all,
>>
>> How can I build the following product with numpy
>>
>> q_i = \varepsilon_{ijk} q_{kj}
>>
>> where  \varepsilon_{ijk} denotes the permutation symbol.
>>
>> Nils
>>
>  Sorry for replying to myself.
> The permutation symbol is also known as the Levi-Civita symbol.
> I found an explicit expression at
> http://en.wikipedia.org/wiki/Levi-Civita_symbol
>
> How do I build the product of the Levi-Civita symbol \varepsilon_{ijk} and
> the two dimensional array
> q_{kj}, i,j,k = 1,2,3 ?
>

Write it out explicitly. It essentially antisymmetrizes q and the three off
diagonal elements can then be treated as a vector. Depending on how q is
formed and the resulting vector is used there may be other things you can do
when you use it in a more general expression. If this is part of a general
calculation there might be other ways of expressing it.

Chuck
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