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 collections of $N=d+...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
25.02.2019
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| Subjects | |
| 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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| DOI: | 10.48550/arxiv.1902.09443 |