# How should the implicit sum $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted?

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

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

• That looks correct to me, even if without any context is not so easy to say. – DarioP Feb 3 '14 at 7:58
• 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. – Dilaton Feb 3 '14 at 8:15
• What would be the alternative? – David Z Feb 3 '14 at 8:38
• More on Einstein notation: physics.stackexchange.com/search?q=Einstein+[notation] – Qmechanic Feb 3 '14 at 8:38
• Thanks. I wanted to make sure since I'm not used to tensors nor Einstein notation. – Anna Feb 3 '14 at 9:14