On the principal minors of Fourier matrices
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915250651004928 |
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| author | Caragea, Andrei Lee, Dae Gwan |
| author_facet | Caragea, Andrei Lee, Dae Gwan |
| contents | For the $N$-dimensional Fourier matrix $\mathcal{F}_N$, we prove that if $N\geq 4$ is square-free, then every $2 \times 2$ and $3\times 3$ principal minor of $\mathcal{F}_N$ is nonzero. We also show that if $N\geq 4$ is not square-free, then $\mathcal{F}_N$ has zero principal minors of all sizes. Moreover, based on numerical experiments, we conjecture that if $N$ is square-free, then all principal minors of $\mathcal{F}_N$ are nonzero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_09793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the principal minors of Fourier matrices Caragea, Andrei Lee, Dae Gwan Functional Analysis 42C15, 42A99, 11C20 For the $N$-dimensional Fourier matrix $\mathcal{F}_N$, we prove that if $N\geq 4$ is square-free, then every $2 \times 2$ and $3\times 3$ principal minor of $\mathcal{F}_N$ is nonzero. We also show that if $N\geq 4$ is not square-free, then $\mathcal{F}_N$ has zero principal minors of all sizes. Moreover, based on numerical experiments, we conjecture that if $N$ is square-free, then all principal minors of $\mathcal{F}_N$ are nonzero. |
| title | On the principal minors of Fourier matrices |
| topic | Functional Analysis 42C15, 42A99, 11C20 |
| url | https://arxiv.org/abs/2409.09793 |