Asymptotically optimal approximate Hadamard matrices
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917089601650688 |
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| author | Alexeev, Boris Jasper, John Mixon, Dustin G. |
| author_facet | Alexeev, Boris Jasper, John Mixon, Dustin G. |
| contents | In this paper, we study approximate Hadamard matrices, that is, well-conditioned $n\times n$ matrices with all entries in $\{\pm1\}$. We show that the smallest-possible condition number goes to $1$ as $n\to\infty$, and we identify some explicit infinite families of approximate Hadamard matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically optimal approximate Hadamard matrices Alexeev, Boris Jasper, John Mixon, Dustin G. Combinatorics Functional Analysis In this paper, we study approximate Hadamard matrices, that is, well-conditioned $n\times n$ matrices with all entries in $\{\pm1\}$. We show that the smallest-possible condition number goes to $1$ as $n\to\infty$, and we identify some explicit infinite families of approximate Hadamard matrices. |
| title | Asymptotically optimal approximate Hadamard matrices |
| topic | Combinatorics Functional Analysis |
| url | https://arxiv.org/abs/2511.14653 |