# Homework Help: 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 $C_{rs}$