# Homework Help: Splitting sigmas

1. Nov 12, 2012

### Bipolarity

1. The problem statement, all variables and given/known data Prove the following statement, where A and B are nxn matrices.

$$Tr(AB) = Tr(BA)$$

2. Relevant equations

3. The attempt at a solution
Using some manipulations, I arrived at
$$\sum^{n}_{p=1}\sum^{n}_{k=1}A_{pk}B_{kp} = \sum^{n}_{p=1}\sum^{n}_{k=1}B_{pk}A_{kp}$$

If I can prove the above, I am done, but I have never worked with double sigma notations before, so any advice folks?

BiP

2. Nov 12, 2012

### Dick

k and p are what are called 'dummy indices'. You can change k to any other letter, like q and you still have a good formula for Tr. Just interchange k and p.

3. Nov 13, 2012

### Bipolarity

Ah, ingenious! Thanks!

BiP