(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that in 2 dimensions a skew-symmetric tensor of second rank is a pseudoscalar and that one of third rank is impossible.

3. The attempt at a solution

A^{11}=A^{22}=0, while A^{12}=-A^{21}, which makes

A= A^{12}+A^{21}, which is certainly skew-symmetric, though I am not sure it is a pseudoscalar since a pseudoscalar is a number, and the tensor should have only one component in this case, or maybe not?

I guess this will help with the next part of the exercise.

Thank you

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Verification of tensor identities

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