Frame Potentials and Orthogonal Vectors
An extension is given of a recent result of Glazyrin, showing that an orthonormal basis \(\{e_{i}\}_{i=1}^{d}\) joined with the vectors \(\{e_{j}\}_{j=1}^{m}\), where \(1\leq m < d\) minimizes the \(p\)-frame potential for \(p\in[1,2\log{\frac{2m+1}{2m}}/\log{\frac{m+1}{m}}]\) over all collection...
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| Published in | arXiv.org |
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| Main Author | |
| Format | Paper |
| Language | English |
| Published |
Ithaca
Cornell University Library, arXiv.org
22.04.2019
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| Online Access | Get full text |
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| Summary: | An extension is given of a recent result of Glazyrin, showing that an orthonormal basis \(\{e_{i}\}_{i=1}^{d}\) joined with the vectors \(\{e_{j}\}_{j=1}^{m}\), where \(1\leq m < d\) minimizes the \(p\)-frame potential for \(p\in[1,2\log{\frac{2m+1}{2m}}/\log{\frac{m+1}{m}}]\) over all collections of \(N=d+m\) vectors \(\{x_1,\dots,x_N \}\) in \(\mathbb{S}^{d-1}\). |
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| ISSN: | 2331-8422 |