What Does \sum_{i,j=1}^n A_{i,j} Mean?

[hbweb500]

I am working on a problem that uses the notation:

$$\sum_{i,j=1}^n A_{i,j}$$

Where A is an (n x n) matrix. I am a little unsure of what the summation is over, due to the odd notation "i,j = 1". My first guess is that this is shorthand for

$$\sum_{i=1}^n \sum_{j=1}^n A_{i,j}$$

But I am wondering if it could also mean the sum over the diagonal elements of the matrix, i.e.:

$$\sum_{i=1}^n A_{i,i}$$

I am guessing it is the first, but I want to make absolutely sure.

 

[LCKurtz]

Yes, your first guess is the standard interpretation.

 

[hbweb500]

Thanks!