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I saw in several places in the numerical linear algebra that the inner product is interpreted as the correlation. However, I don't see why they do it. Please, can you explain to me what is the relation between correlation and the inner product?

I know that if the inner product is equal to $0$ then the vectors are linearly independent.

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    $\begingroup$ In a sense, correlation can be interpreted as being related to an inner product: covariance defines an inner product of probability distributions, and the correlation is related to this. However, you seem to be asking whether inner products can generally be interpreted as giving you the correlation of two distributions, and the answer to this is no. I would suspect that in your sources that say "the inner product is interpreted as the correlation", they are referring to correlation in an informal sense, i.e. that the inner product tells you "the extent to which two vectors are correlated" $\endgroup$
    – Ben Grossmann
    Commented May 11, 2020 at 13:36
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    $\begingroup$ You could say that taking the inner product of two unit vectors gives you an analog to the statistical correlation for pairs of vectors in an inner product space. $\endgroup$
    – Ben Grossmann
    Commented May 11, 2020 at 13:39
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    $\begingroup$ math.stackexchange.com/q/1536234/321264 $\endgroup$
    – StubbornAtom
    Commented May 11, 2020 at 20:27

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