# Vector Problem. Free and dummy indices?

1. Oct 3, 2011

### P-Jay1

(ABC)ij =Xk Xl AikBklClj where x is the sum of

In the above equation which are the dummy indices and which are the free indices?

I think i and j are free, and k and l are dummy. But im not surre!

2. Oct 3, 2011

### vela

Staff Emeritus
That's right.

3. Oct 4, 2011

### P-Jay1

The above is a system of equations. I dont know how many it holds though. Is it 3? How do i show this?

4. Oct 4, 2011

### vela

Staff Emeritus
You have one equation for each possible combination of the free indices, e.g. i=1, j=1; i=2, j=1; etc. How many does that give you?

5. Oct 6, 2011

### P-Jay1

Thankyou vela I see now! Ive got one last question:What are the ranges of summation over k and l?

6. Oct 6, 2011

### HallsofIvy

Staff Emeritus
It is impossible to answer that, just as it is impossible to say exactly how many equations that represents, without knowing the dimension of the problem. If two dimensional, all indices range from 1 to 2, if three dimensional, from 1 to 3. If four dimensional, from 1 to 4, etc.