I'm trying to grasp Levi-civita and Kronecker del notation to use when evaluating geophysical tensors, but I came across a few problems in the book I'm reading that have me stumped.
1) $\delta_{i\,j}\delta_{i\,j}$
2) $\delta_{i\,j} \epsilon_{i\,j\,k}$
I have no idea how to approach evaluating these properties. Without knowing i, j, or k, how would I approach? I don't feel confident using the notation further until I can understand these properties.
$\delta_{ij}=\begin{cases}1 & \text{if } i=j \\ 0 & \text{otherwise}\end{cases}$
https://en.m.wikipedia.org/wiki/Kronecker_delta
$\epsilon_{ijk}=\begin{cases} sgn(ijk) & \text{as a permutation, if } i,j,k \text{ are different} \\ 0 & \text{otherwise}\end{cases}$
https://en.m.wikipedia.org/wiki/Levi-Civita_symbol
And of course repeated indices (up-down and down-up) are to be summed over (https://en.m.wikipedia.org/wiki/Einstein_notation)
Thus for example your second expression is identically zero