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[itex]x_{i}y_{i}[/itex]

I create a sum of terms such that in each term the subscripts are the same i.e.

[itex]x_{1}y_{1}+x_{2}y_{2}+x_{3}y_{3}+...[/itex]

But now when I look at understanding summation convention applied to the generalised Hooke's law:

[itex]\tau _{ik}=C_{ikrs}E_{rs}[/itex]

I'm a bit unsure what this means. I understand that C is a tensor with 81 components and that by applying the summation convention I should get linear combinations for every [itex]\tau[/itex] component (I think). But as for applying summation convention to see what exactly those sums look like I'm unsure.

The statement below doesn't seem to help my understanding either

"[itex]\tau _{ik}[/itex] is a linear combination of all strain components [itex]E_{ik}[/itex]"

Any assistance would be appreciated.

## The Attempt at a Solution

I could hazard I guess and say I only sum when r or s equals i or k, and when r=s and i=k. Still unsure if that is correct though.