Suppose that $n$-dimensional random vector $Y$ has covariance matrix $\Sigma$. It is well known that for any $a\in\mathbb{R}^n$ we have

\begin{align} var(a^TY)=a^T\Sigma a. \end{align}

Is there any similar interpretation for scalar product induced by $\Sigma$, i.e. for expressions of the form

\begin{align} a^T\Sigma b \end{align} given $a,b \in \mathbb{R}^n$?

Thank you for any comments.


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