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A $k\times k$ matrix of correlations between all pairs of $k$ random variables. All its diagonal elements are equal to one.

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Is it possible that 3 vectors have all negative pairwise correlations?

Given three vectors $a$, $b$, and $c$, is it possible that correlations between $a$ and $b$, $a$ and $c$, and $b$ and $c$ are all negative? I.e. is this possible? \begin{align} \text{corr}(a,b) < 0\ …
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