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# Suffix notation (vector calculus) Watch

1. I'm asked to prove, using suffix notation, the following identity:

I know that , , and so on... I also know that where F is some vector field and that and so on.

I'm struggling to link the definitions above, however. For example, for I'm struggling to show this in suffix notation. I tried writing it as . Is it wrong to sum over a different index l or can I sum it over, say, i as well?

I also tried writing out the other terms in suffix notation, and got:

again, is it wrong to sum over l and should I sum over i/j/k instead?

Thanks for any clarification
2. (Original post by trm90)
You can't write that. The quantity inside the bracket is already a scalar, so you can't have a further index on it. It's .
3. (Original post by Zhen Lin)
You can't write that. The quantity inside the bracket is already a scalar, so you can't have a further index on it. It's .
Silly of me to forget that (especially how the whole point of suffix notation is to make vectors look cleaner :P), thanks very much!
4. Sorry to bump this thread, just one more question

I have to use suffix notation again to show:

I next evaluated the last term in the equation:

thus

Combining the two terms together (taking into account the negative sign in nabla^2 A) I should get

Next I figured I'd go about evaluating the left hand side in hopes that its final expression will lead to a summation similar to above.

I think I might have got a little lost here though...

I can kind of visualise the answer from here as if j = k = l = m then the bracket containing the delta comes to 1-1 and in my RHS there are no expressions which involve dA_i / dx_i in it. I am, however, struggling to do the last line or two which proves that my expression above works? I can't really seem to understand what it means to have an 'm' suffix next to my differentiation term... I've also toyed around with different combinations of j, k, l, m and can't seem to get much.

any help much appreciated.
5. (Original post by trm90)
It's the same mistake again - you can't have a subscript on a scalar! It's .
6. (Original post by trm90)
thus
Be careful when you write something like this - you mean to say the i-th component of the vector on the LHS is equal to the RHS.
7. (Original post by Zhen Lin)
It's the same mistake again - you can't have a subscript on a scalar! It's
Hmm, I'm definitely not understanding it now then; where in my expression was I summing a scalar?

Also, I'm looking at the new expression and it'sstarting to make sense now So that means the product of the epsilon terms will be

yes?
8. (Original post by trm90)
Hmm, I'm definitely not understanding it now then; where in my expression was I summing a scalar?
— the expression inside the brackets is a scalar. (To be precise, it's a family of scalars indexed by i.) It doesn't have any components to be indexed by m.

On the other hand, is a family of vectors indexed by i, so you can have a further subscript m to indicate its components: in particular, . However, mixing vectors and suffix notation like this is considered bad form and should be avoided.

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Updated: December 29, 2010
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