Index Notation and Kronecker Delta

[Lonely Lemon]

Homework Statement

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

$C_{ns}\delta_{rn}$

Homework Equations

The Attempt at a Solution

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

 

[Pengwuino]

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

 

[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...

 

[Pengwuino]

Well what's the definition of the Kronecker delta?

 

[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

 

[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 $C_{rs}$