# Summation notation problem

1. Jan 9, 2014

### SergeantAngle

Hi

I have a text book which uses the notation:

$\sum\limits_{i\neq j}^N a_i a_j$

I can't find anywhere what this actually means. Is it equivalent to:

$\sum\limits_{i}^N \sum\limits_{j}^N a_i a_j$

where j can't equal i?

Thanks.

2. Jan 9, 2014

### 1MileCrash

It's just the sum of all $a_{i}a_{j}$ when i does not equal j.

You can put pretty much any condition you want in that space, though I see it abused more often for unions and intersections of sets.

3. Jan 9, 2014

### Staff: Mentor

Yes, pretty much. For example, if N = 3, and both indexes start at 1, then the summation expands to a1a2 + a1a3 + a2a1 + a1a3 + a2a3 + a3a2. The terms that are omitted are a12, a22, and a32.

4. Jan 10, 2014

### SergeantAngle

Okay, thanks.