# Antisymmetric and symmetric part of a general tensor

## 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

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

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)

## Answers and Replies

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