I am trying to learn about vector/tensor math and stumbled across these exercises in my textbook.
(1) Evaluate the expression $\delta _j^i \delta _i^j $
(2) Evaluate the expression $\delta _i^i \delta _j^j $
(3) Simplify the expression $S_i S^j \delta _j^i $
How would one go about evaluating these? Is it as simple as contracting the expressions (where (!) would cancel out completely) or is it necessary to look at the identity matrices in the cases where i=j and i=/=j?
You need to specify the range of the index.
Assuming it is $n$, expression (1) $=n$, while expression (2) $=n^2$. Expression (3) $=S_iS^i$.