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I am trying to get a "feel" for the covariance matrix. I know that $v_iCov(X)v_j$ gives the covariance between $X$ projected along $v_i$ and $v_j$. I'm curious if there's a similar intuitive interpretation of $Cov(X)v$ for any vector $v$.

Edit:

$X$ is a vector of $n$ random variables and $v_i, v_j, v \in R^n$

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  • $\begingroup$ What are $v_i$, $v_j$ and $v$? $\endgroup$
    – develarist
    Jan 26 at 22:42
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    $\begingroup$ A good linear algebra textbook will provide helpful explanations of dual spaces, which is the underlying fundamental concept here. $\endgroup$
    – whuber
    Jan 27 at 15:04
  • $\begingroup$ "Covariance is the difference between the average product and the product of averages" $\endgroup$
    – John Stud
    Jan 28 at 15:12
  • $\begingroup$ @whuber that's really interesting can you point to any source? I have learned about dual spaces but I don't know how they relate. $\endgroup$ Jan 31 at 6:19
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    $\begingroup$ Mervyn Stone (1987), "Coordinate-Free Multivariable Statistics", Clarendon Press, Oxford. Michael Wichura (2006), "The Coordinate-Free Approach to Linear Models," Cambridge Univ. Press. $\endgroup$
    – whuber
    Jan 31 at 15:35

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