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I'm trying to work out the following, but have gotten myself a bit confused I'm still getting to grips with using indices:

if I have $$\bar{\nabla} \times (\bar{a}\bar{x})\bar{b}$$

I re wrote this as: $$\epsilon_{ijk}\partial_j(a_ix_j)b_k$$

But I don't really know what to do now to expand/simplify it? Any guidance would be much appreciated.

Sarah Jayne
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  • what's $\bar \nabla$ and $\bar a$ ... ?? you working on tensors ?? covariant derivatives? – S L May 24 '14 at 18:24
  • It's just to denote that they are vectors (I think) I've figured it out now though, thank you. I do have another quick question though if you're willing to help? (Don't want to create a new question for such a little thing) If I have a tensor of rank $(2,0)$, how do I formally define that - is it just that we have a tensor with two 'upstairs' elements? – Sarah Jayne May 25 '14 at 08:32
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    yes, contravariant we have downstairs $a_{ij}$ contravariant we have upstairs $a^{ij}$ – S L May 25 '14 at 08:36

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