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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.16432 |
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| _version_ | 1866916802235203584 |
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| author | García-Marco, Ignacio Márquez-Corbella, Irene Seco, Daniel |
| author_facet | García-Marco, Ignacio Márquez-Corbella, Irene Seco, Daniel |
| contents | We disprove a conjecture by Ye and Lim, by showing that there are $3 \times 3$ complex matrices which can't be expressed as the product of two Toeplitz matrices of the same size. We also improve previous estimates by Ye and Lim on the minimum number of Toeplitz matrices needed to factor any $n \times n$ matrix, for low values of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the minimum number of Toeplitz factors of a matrix García-Marco, Ignacio Márquez-Corbella, Irene Seco, Daniel Commutative Algebra 15B05 We disprove a conjecture by Ye and Lim, by showing that there are $3 \times 3$ complex matrices which can't be expressed as the product of two Toeplitz matrices of the same size. We also improve previous estimates by Ye and Lim on the minimum number of Toeplitz matrices needed to factor any $n \times n$ matrix, for low values of $n$. |
| title | On the minimum number of Toeplitz factors of a matrix |
| topic | Commutative Algebra 15B05 |
| url | https://arxiv.org/abs/2506.16432 |