- #1

- 560

- 2

## Main Question or Discussion Point

I've seen it stated several times that a general covariant or contravariant tensor of rank n can be separated into it's symmetic and antisymmetric parts

[tex] T^{\mu_1 \ldots \mu_n} = T^{[\mu_1 \ldots \mu_n]} + T^{(\mu_1 \ldots \mu_n)}[/tex]

and this is easy to prove for the case n=2, but I don't see how to prove it for a general n. Could anyone help me out?

(suspect this has been posted in the wrong forum, but I also suspect that the general relativists can answer this question as good or better than the mathematicians)

[tex] T^{\mu_1 \ldots \mu_n} = T^{[\mu_1 \ldots \mu_n]} + T^{(\mu_1 \ldots \mu_n)}[/tex]

and this is easy to prove for the case n=2, but I don't see how to prove it for a general n. Could anyone help me out?

(suspect this has been posted in the wrong forum, but I also suspect that the general relativists can answer this question as good or better than the mathematicians)