# Does this parameter of two sequence have a name?

Let $a=a_1,a_2,...,a_n$ and $b=b_1,b_2,...,b_n$ be two sequence of real numbers. Define

$$D(a,b) := \sum_{\{i,j\}}\sum_{\{k,l\}}{(|a_i-a_j||b_k-b_l|-|a_k-a_l||b_i-b_j|)^2} .$$

Does this parameter have a name? I just need some reference if there's any.

• Isn't this always zero? – Wojowu Feb 10 '17 at 16:31
• Every term $|a_p-a_q||b_r-b_s|$ appears twice, once with a positive sign when $\{i,j\}=\{p,q\},\{k,l\}=\{r,s\}$, once with a negative sign when $\{i,j\}=\{r,s\},\{k,l\}=\{p,q\}$. – Wojowu Feb 10 '17 at 16:41
• @Wojowu: Yes, you are right. Thanks. I have a typo. I edit my question. – b.a Feb 10 '17 at 16:48
• since it is a sum of squares it can only be zero if every summand is zero – user35593 Feb 10 '17 at 22:28