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I am working on a "tensor gymnastics" exercise, and have arrived at the following line to simplify:

$\delta_{ik} y^{i} X_{ij}$

where $\delta_{ik}$ is the Kroenecker delta. Does this simplify to:

$y^{k} X_{kj}$, i.e., replace all of the $i's$ with $k's$, or just apply to one of the $y^i$ or $X_{ij}$?

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"Tensor gymnastics" cannot change the number of times a given index appears, which should be two for a dummy index that is summed over or one for a standard index. As you have three $i$'s in your expression, you have probably made a mistake in one of the lines above.

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