More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909359710142464 |
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| author | Iverson, Joseph W. Jasper, John Mixon, Dustin G. |
| author_facet | Iverson, Joseph W. Jasper, John Mixon, Dustin G. |
| contents | We introduce a new infinite family of $d\times 2d$ equiangular tight frames. Many matrices in this family consist of two $d\times d$ circulant blocks. We conjecture that such equiangular tight frames exist for every $d$. We show that our conjecture holds for $d\leq 165$ by a computer-assisted application of a Newton-Kantorovich theorem. In addition, we supply numerical constructions that corroborate our conjecture for $d\leq 1500$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$ Iverson, Joseph W. Jasper, John Mixon, Dustin G. Metric Geometry Combinatorics Functional Analysis We introduce a new infinite family of $d\times 2d$ equiangular tight frames. Many matrices in this family consist of two $d\times d$ circulant blocks. We conjecture that such equiangular tight frames exist for every $d$. We show that our conjecture holds for $d\leq 165$ by a computer-assisted application of a Newton-Kantorovich theorem. In addition, we supply numerical constructions that corroborate our conjecture for $d\leq 1500$. |
| title | More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$ |
| topic | Metric Geometry Combinatorics Functional Analysis |
| url | https://arxiv.org/abs/2410.17379 |