The maximal angle between 3 × 3 copositive matrices
Résumé
In 2010, Hiriart-Urruty and Seeger posed the problem of finding the maximal possible angle θn between two copositive matrices of order n. They proved that θ2 = 3π/4. In this paper, we study the maximal angle between two copositive matrices of order 3. We show that θ3 = 3π/4 and give all possible pairs of matrices achieving this maximal angle. The proof is based on case analysis and uses optimization and basic linear algebra techniques.