This work uncovers criteria for identifying dependent sets and explores bases in determinantal matroids, suggesting avenues for rank matrix completion.
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.
No takes yet. Share an insight, caveat, or question.
Nicklasson et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: