  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 $n \geq
2$. In this note we disprove their conjecture by showing that $\lim_{n
\rightarrow \infty}{\theta_{\max}(\mathcal{C}_{n})}=\pi$. 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.
