Meaning of notation: $x_{l,L}$

Question

The question is show that $$x_{l,L}X_{L,k}=\delta _{kl}$$ but what does that notation even mean?? The topic of this is continuum mechanics.

Answer 1

The notation uses the Einstein summation convention: sum over same indices.
The Kronecker delta $\delta_{kl}$ is the identity matrix.

This could be the component form of the matrix product of matrices $x=(x_{lm})$ and $X=(X_{jk})$: $$ x X = I \Rightarrow \\ (x X)_{ik} = x_{lL} X_{Lk} = \delta_{kl} = \delta_{lk} = (I)_{lk} $$