[Numpy-discussion] permutation symbol
Charles R Harris
charlesr.harris at gmail.com
Tue Jun 30 12:27:05 EDT 2009
On Tue, Jun 30, 2009 at 5:11 AM, Nils Wagner
<nwagner at iam.uni-stuttgart.de>wrote:
> On Tue, 30 Jun 2009 11:22:34 +0200
> "Nils Wagner" <nwagner at 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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