- #1
Telemachus
- 835
- 30
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:
[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?
[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?