The maximal angle between $3 \times 3$ copositive matrices
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929663564054528 |
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| author | Gourion, Daniel |
| author_facet | Gourion, Daniel |
| contents | In 2010, Hiriart-Urruty and Seeger posed the problem of finding the maximal possible angle $θ_n$ between two copositive matrices of order $n$. They proved that $θ_2=\frac{3}{4}π$. In this paper, we study the maximal angle between two copositive matrices of order 3. We show that $θ_3=\frac{3}{4}π$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The maximal angle between $3 \times 3$ copositive matrices Gourion, Daniel Optimization and Control In 2010, Hiriart-Urruty and Seeger posed the problem of finding the maximal possible angle $θ_n$ between two copositive matrices of order $n$. They proved that $θ_2=\frac{3}{4}π$. In this paper, we study the maximal angle between two copositive matrices of order 3. We show that $θ_3=\frac{3}{4}π$ 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. |
| title | The maximal angle between $3 \times 3$ copositive matrices |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.03773 |