In algebra of random variables, the symbolic rule for computing variance of random variable $X\in\mathbb{R}^{n\times p}$ multiplied by a coefficent vector, $a\in\mathbb{R}^p$, is
$$\text{Var}(X\cdot a) = a^\top \text{Var}(X) a = a^\top \Sigma a $$ where $\Sigma$ is the covariance matrix. What explains vector $a$ coming out twice, i.e. the full derivation?
Given the above, what is the skewness algebra of random variables, and kurtosis algebra of random variables, i.e. derivation of the two expressions below?
$$\text{Skew}(X\cdot a) =? \hspace{3cm} \text{Kurt}(X\cdot a)=?$$
