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Consider the maximization problem $$\text{maximize} \quad Q(x)= \sum_{i<j} a_{ij} x_i x_j \quad \text{subject to} \quad \sum_{i}x_i^2=1,$$ and let $M$ be maximum value obtained by $Q$ under such constraint. Suppose that $$\begin{cases} a_{ij}=0 & \text{if i+j\equiv 0\mod 2,} \\ a_{ij}>0 & \text{if i+j\equiv 1\mod 4,} \\ a_{ij}<0 & \text{if i+j\equiv 3\mod 4.} \end{cases}$$ I […]