$C$ is a 3x3x3x3 tensor. How should the expression $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted? This is my guess:

$$ \sum_{i=1}^3\sum_{j=1}^3 \sum_{k=1}^3\sum_{l=1}^3 C_{ijkl}u_{i,j}u_{k,l} $$

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    $\begingroup$ That looks correct to me, even if without any context is not so easy to say. $\endgroup$ – DarioP Feb 3 '14 at 7:58
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    $\begingroup$ Yes, applying Einstein summation the sums are implicitely assumed. More correctly, one of the two summed over indices should be an upper (contravariant) index and the other one a lower (covariant) index. $\endgroup$ – Dilaton Feb 3 '14 at 8:15
  • $\begingroup$ What would be the alternative? $\endgroup$ – David Z Feb 3 '14 at 8:38
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    $\begingroup$ More on Einstein notation: physics.stackexchange.com/search?q=Einstein+[notation] $\endgroup$ – Qmechanic Feb 3 '14 at 8:38
  • $\begingroup$ Thanks. I wanted to make sure since I'm not used to tensors nor Einstein notation. $\endgroup$ – Anna Feb 3 '14 at 9:14

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