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Expanding Kroniker Delta

wmccunes

New member
Jan 30, 2013
8
Hi, I'm working on a problem stated as:
Expand the following expression and simplify where possible
$$
\delta_{ij}\delta_{ij}
$$

I'm pretty sure this is correct, but not sure that I am satisfying the expand question. I'm not up to speed in linear algebra (taking a continuum mechanics course) - the question could be asking for $\hat{e}$ or matrix type expansion...

my solution:
\begin{alignat}{3}
\delta_{ij}\delta_{ij} & = & \delta_{ij}\delta_{ji}\\
& = & \delta_{ii}\\
& = & 3
\end{alignat}

Any suggestions for how to expand - or does this answer the question?
Thanks, Jason
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,193
Your working is correct if you're in 3 dimensions and you're using the Einstein summation convention.
 

wmccunes

New member
Jan 30, 2013
8
Thanks. What do you think they mean by "Expand", then?
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,193
When you expand a sum like that, you're writing out every term, essentially. And then because they combine as you've shown, it collapses down to a nice compact number.