The Determinantal Matroid
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912810012770304 |
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| author | Nicklasson, Lisa Tsakiris, Manolis C. |
| author_facet | Nicklasson, Lisa Tsakiris, Manolis C. |
| contents | We study the algebraic matroid induced by the ideal of (r+1)-minors of a matrix of variables over a field. This is inherently connected to the bounded-rank matrix completion problem, in which the aim is to complete a partially observed rank r matrix. We give criteria that detect dependent sets in the matroid, we describe a family of bases of the matroid, and we study the question of unique completability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18222 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Determinantal Matroid Nicklasson, Lisa Tsakiris, Manolis C. Commutative Algebra Combinatorics 14M12, 15A83, 13C40, 05B35 We study the algebraic matroid induced by the ideal of (r+1)-minors of a matrix of variables over a field. This is inherently connected to the bounded-rank matrix completion problem, in which the aim is to complete a partially observed rank r matrix. We give criteria that detect dependent sets in the matroid, we describe a family of bases of the matroid, and we study the question of unique completability. |
| title | The Determinantal Matroid |
| topic | Commutative Algebra Combinatorics 14M12, 15A83, 13C40, 05B35 |
| url | https://arxiv.org/abs/2502.18222 |