Let $X = (X_1,...,X_n)$ be a vector of $n$ random variables. Consider the following maximization problem:
$\max\limits_{a,b} \;\mathrm{Cov}(a\cdot X, b \cdot X)$ under the constraint that $\|a\|_2 = \|b\|_2 = 1$.
($a \cdot X$ is the dot product between $a$ and $X$). Would it be true that there is a solution to this maximization problem such that $a = b$?
Thanks.