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#### Article Title

#### Keywords

Copositive matrix, Convex cone, Critical angle, Strongly regular graph, Symmetric nonnegative inverse eigenvalue problem

#### Abstract

Hiriart-Urruty and Seeger have posed the problem of finding the maximal possible angle θ_{max}(C_n) between two copositive matrices of order n [J.-B. Hiriart-Urruty and A. Seeger. A variational approach to copositive matrices. SIAM Rev., 52:593–629, 2010.]. They have proved that θ_{max}(C_2) = (3/4)pi and conjectured that θ_{max}(C_n) is equal to (3/4)pi for all n ≥ 2. In this note, their conjecture is disproven by showing that lim_{n→∞} θ_{max}(C_n) = pi. The proof uses a construction from algebraic graph theory. The related problem of finding the maximal angle between a nonnegative matrix and a positive semidefinite matrix of the same order is considered in this paper.

#### Recommended Citation

Goldberg, Felix and Shaked-Monderer, Naomi.
(2014),
"On the maximal angle between copositive matrices",
*Electronic Journal of Linear Algebra*,
Volume 27.

DOI: http://dx.doi.org/10.13001/1081-3810.2842