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I hope that you will not mind if I do not explain the background of this formula. The problem which I encounter is probably a simple one: What does the huge $\large \times$ mean and why is it written like a sigma? I had no clue how to search for this.

My understanding is: $(l_1, ..., l_{|M|})$ is a set that is defined by counting from $j$ up to $|M|$ and that projects on $\mathbb{R}$ while using $r(m_i, m_j)$ as a function for $l_j$.

Is that correct?

Thank you very much!

$$\large{L_i=(l_1, \ldots l_{|M|})\in \mathop{\huge \times}^{|M|}_{j=1}\Bbb R, \,l_j=r(m_i, m_j)}$$

Git Gud
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Xiphias
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  • looks like an |M|-fold cartesian product. I haven't seen that notation before, though. – Tyler Nov 03 '13 at 17:40
  • Yes, indeed, a Cartesian product. There is some fixed underlying function $r:\mathbb R\times \mathbb R\to \mathbb R$, and $L_i$ is just the ordered set of images $l_j=r(m_i,m_j)$ ocurring in the $j$-th component of $L_i$. For fixed $i$, $m_i$ is also fixed, while $m_j$ varies. – Doc Nov 03 '13 at 17:46
  • Git Gud, thank you for silently improving my notation :-) I stumbled upon it when reading a text about pearson correlation coefficient. Pairs of $m_i$ are compared with each other. – Xiphias Nov 03 '13 at 17:53

1 Answers1

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It's probably an $|M|$-fold Cartesian product. This link to the TeX stackexchange supports this interpretation.

Community
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Tyler
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