My Math Forum calculation of the sum

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 August 1st, 2012, 07:31 PM #1 Member   Joined: Aug 2011 Posts: 71 Thanks: 0 calculation of the sum Let $x=(x_1, ..., x_{2n})$ be real vector How to represent the following sum in terms of the $l_2$ norm of vector $x$: $\sum_{i=1}^n\sum_{j=n+1}^{2n}(x_i-x_j)^2$. Thank you.
 August 10th, 2012, 03:38 AM #2 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 Re: calculation of the sum Hey Anton29. Are you having trouble evaluating the sum or deriving the sum corresponding to the norm between two vectors?
 August 23rd, 2012, 10:33 PM #3 Member   Joined: Aug 2011 Posts: 71 Thanks: 0 Re: calculation of the sum I wanted to reperesent the sum in terms of l_2 norms, but turns out that one can only bounded it. I've got it.

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