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For publication and/or presentation purposes, is there a symbol to denote the calculation of a correlation between two vectors?

Obviously, for the value of the correlation is symbolically represented using $\rho$ for Pearson's or Spearman's, and $\tau$ for Kendall's, but what is the appropriate way (if any) to present the calculation without the entire formula?

For instance, if I want to report that I calculated the Pearson's correlation between two vectors, $x$ and $y$, I would image writing it as:

$\rho$ = $x$ (some symbol) $y$

The same way to represent the product of $x$ and $y$ would be written $x$ x $y$, or the sum by $x$ + $y$ or $\Sigma xy$.

Would $\rho$ = $cor(x,y)$ be correct?

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The pearson correlation coefficient is defined as

corr

like you already mentioned (correlation with two 'r' as far as i know). For using the correlation with a vector it should be simple enough to mark them as vectors. Use the notation from the ISO 80000-2:2009 [1] for this.

bold italic serif:

one way to notate

or with vector arrows

vector arrows

i guess you are already using one of the notations for your vectors, so take the one you are already using in your paper for keeping your style.

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