The Determinantal Matroid
Commutative Algebra
2026-01-09 v2 Combinatorics
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.
Cite
@article{arxiv.2502.18222,
title = {The Determinantal Matroid},
author = {Lisa Nicklasson and Manolis C. Tsakiris},
journal= {arXiv preprint arXiv:2502.18222},
year = {2026}
}