# Tensor gymnastics

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 $$X_{ij}$$?

"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.