Symmetrizing and skew symmetrizing tensors

1. Oct 28, 2007

quasar_4

I understand that all rank 2 tensors can be decomposed into a symmetric and a skew symmetric part, but I don't really understood how this is done. It has something to do with permutations of the indices, I guess, but I never learned anything about what a permutation is. Can anyone explain how one would go about symmetrizing (without assuming I have any knowledge of how to permute something)?

2. Oct 28, 2007

robphy

Just do it...
$$A_{ab}=\frac{A_{ab}+A_{ba}}{2}+\frac{A_{ab}-A_{ba}}{2}$$

To elaborate, for any pair of vectors $$u^a$$ and $$v^b$$
$$A_{ab}u^av^b=\frac{A_{ab}+A_{ba}}{2}u^av^b+\frac{A_{ab}-A_{ba}}{2}u^av^b$$

Last edited: Oct 28, 2007