Index Notation and Kronecker Delta

1. Jul 17, 2011

Lonely Lemon

1. The problem statement, all variables and given/known data

Simplify the following expressions involving the Kronecker delta in N dimensions. Where possible, write the final result without indices.

$C_{ns}\delta_{rn}$

2. Relevant equations

3. The attempt at a solution

I know Kronecker delta is symmetric but that doesn't seem to help. Is this undefined?

2. Jul 17, 2011

Pengwuino

Hmm this sounds too simple, is there something special about C?

3. Jul 17, 2011

Lonely Lemon

There's nothing special about C, the exercise is to just get us used to index notation and what it means I think but I'm struggling a bit. The next question is:

$$A_{ij}B_{nk}C_{rs}\delta_{jr}\delta_{sn}\delta_{ik}$$

but I can't do that until I figure out how to work with delta above...

4. Jul 17, 2011

Pengwuino

Well what's the definition of the Kronecker delta?

5. Jul 17, 2011

Lonely Lemon

It's the identity matrix, but $$\delta_{rn}$$ could be either 0 or 1 depending on if r=n or r=/=n...

EDIT r=/=n

Last edited: Jul 17, 2011
6. Jul 17, 2011

Pengwuino

So if you have something like $C_{ns}\delta_{rn}$, that means this term is only non-zero when r=n so you can simplify the expression as $C_{rs}$