Hello. I'm new to this forum. I'm starting a PhD – it's going to be a big long journey through the jungle that is CFD. I would like to arm myself with some tools before entering. The machete is Cartesian Tensors.(adsbygoogle = window.adsbygoogle || []).push({});

I know the rules regarding free suffix's and dummy suffixes, but I'm having trouble proving the substitution rule:

δ_{i j}δ_{j k}= δ_{i k}

Assuming a range of 3 for each component, I will choose that the free suffix's have the following values: i=3, k=1. Therefore, using the implicit summation rule for the dummy index:

δ_{i j}δ_{j k}= δ_{3 1}δ_{1 1}+ δ_{3 2}δ_{2 1}+ δ_{3 3}δ_{3 1}= ?

Is my expansion correct?

Many thanks.

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# Summation Convention – Substitution Rule

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