I need to understand what the summation below mean. I specifically do not understand the $i<j$ below the summation.
$$\sum_{\substack{
i<j}}^{N} d_{ij}$$
Insight about the equation There are $N$ vectors and $d_{ij}$ is the Euclidean distance between two vectors $i,j \in N $
So if $N=5$ how would the summation work. I would be grateful if it could be explained in numbers so I exactly know how the summation happen.
Additional Information: I encountered this notation in this paper. Looking at your answers and the content of the paper I think the meaning intended is
$$\sum_{j = 1}^{N} \sum_{i<j} d_{ij} $$
Final edit: There are a number of answers which fully explains the notation. Since I have to choose one answer as the best I had to choose the one which explains the notation in detail and thank you all for answering.
Best Answer
I think it should be written as
$$\sum_{1\leq i < j \leq N} {d_{ij}}. $$
This way, it's clear that you sum over all $i,j$ satisfying the inequality $1\leq i < j \leq N$.
If $N=5$, this is equal to
$$d_{12} + d_{13} + d_{14} + d_{15} + d_{23} + d_{24} + d_{25} + d_{34} + d_{35} + d_{45}.$$