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.

  • $\begingroup$ Isn't this always zero? $\endgroup$ – Wojowu Feb 10 '17 at 16:31
  • $\begingroup$ 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 $\{i,j\}=\{r,s\},\{k,l\}=\{p,q\}$. $\endgroup$ – Wojowu Feb 10 '17 at 16:41
  • $\begingroup$ @Wojowu: Yes, you are right. Thanks. I have a typo. I edit my question. $\endgroup$ – b.a Feb 10 '17 at 16:48
  • $\begingroup$ since it is a sum of squares it can only be zero if every summand is zero $\endgroup$ – user35593 Feb 10 '17 at 22:28

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.