On the maximum angle between copositive matrices

Hiriart-Urruty and Seeger have posed the problem of finding the maximal possible angle ${\theta }_{\max }({\mathcal{C}}_n)$ between two copositive matrices of order $n$. They have proved that ${\theta }_{\max }({\mathcal{C}}_2)=\frac{3}{4}\pi$ and conjectured that ${\theta }_{\max }({\mathcal{C}}_n)$ is equal to $\frac{3}{4}\pi$ for all $n \geq 2$\mathrm{.}Inthisnotewedisprovetheirconjecturebyshowingthat$\lim_{n \rightarrow \infty}{\theta_{\max}($\mathcal{C}$_{n})}=\pi$. Our proof uses a construction from algebraic graph theory. We also consider the related problem of finding the maximal angle between a nonnegative matrix and a positive semidefinite matrix of the same order.