{"paper":{"title":"On the maximum angle between copositive matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Goldberg, Naomi Shaked-Monderer","submitted_at":"2013-07-29T09:53:42Z","abstract_excerpt":"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 n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7519","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}