# Scalar product induced by covariance matrix

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.