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arXiv · 2502.18222

The Determinantal Matroid

Lisa Nicklasson·Manolis C. Tsakiris
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Abstract

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.

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Lisa Nicklasson, Manolis C. Tsakiris. 2025-02-25. The Determinantal Matroid. https://arxiv.org/abs/2502.18222

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