Let $\{X_i\}$ be an iid collection of standard normal $(N(0,1))$ random variables . Let $X = (X_1,\ldots,X_n)$, and consider a function of the form $f(X) = \max(A\cdot X)$, where $A$ is some symmetric, positive-definite matrix.

I'm trying to estimate the variance of $f(X)$, and was wondering if someone could give me references for this. This should fall under standard extreme value theory, but things are quite correlated here.