# Homework Help: Kronecker Delta

1. Mar 14, 2010

### Hendrick

1. The problem statement, all variables and given/known data
Simplify/Evaluate these expressions involving the Kronecker delta, using Einstein's summation convention:
a)$$\delta_{qr}$$$$\delta_{rp}$$$$\delta_{pq}$$
b)$$\delta_{pp}$$$$\delta_{qr}$$$$\delta_{rq}$$

2. Relevant equations
$$\delta_{ij}$$=0 when i =/= j
$$\delta_{ij}$$=1 when i = j

3. The attempt at a solution
a)$$\delta_{qr}$$$$\delta_{rp}$$$$\delta_{pq}$$
=$$\delta_{qp}$$$$\delta_{pq}$$
=$$\delta_{qq}$$ = 3 (summation over repeated q)

b)$$\delta_{pp}$$$$\delta_{qr}$$$$\delta_{rq}$$
=$$\delta_{pp}$$$$\delta_{qq}$$
=(3)(3)
=9
[Am I actually able to evaluate the $$\delta_{qr}$$$$\delta_{rq}$$ part before the $$\delta_{pp}$$ part, I mean you can't do that with matrices... :S]

Thank you

2. Mar 14, 2010

### phyzguy

I think what you did is correct. If you think of them as matrices, remember they are identity matrices, so they commute with everything, so the order does not matter.