I have to demonstrate that if [tex]A^{rs}[/tex] is an antisymmetric tensor, and [tex]B_{rs}[/tex] is a symmetric tensor, then the product:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]A^{rs}B_{rs}=0[/tex]

So I called the product:

[tex]C^{rs}_{rs}=A^{rs}B_{rs}=-A^{sr}B_{sr}=-C^{rs}_{rs}[/tex]

In the las stem I've changed the indexes, because it doesn't matters which is which, but I'm not sure this is fine (because I think r and s could have have associated differents values in the sum).

Then

[tex]2C^{rs}_{rs}=2A^{rs}B_{rs}=0[/tex]

Is this ok?

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# Homework Help: Tensor product demonstration

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