English

Fractional Minimal Rank

Functional Analysis 2017-10-23 v1

Abstract

The notion of fractional minimal rank of a partial matrix is introduced, a quantity that lies between the triangular minimal rank and the minimal rank of a partial matrix. The fractional minimal rank of partial matrices whose bipartite graph is a minimal cycle are determined. Along the way, we determine the minimal rank of a partial block matrix with invertible given entries that lie on a minimal cycle. Some open questions are stated.

Keywords

Cite

@article{arxiv.1710.07343,
  title  = {Fractional Minimal Rank},
  author = {Ben W. Grossmann and Hugo J. Woerdeman},
  journal= {arXiv preprint arXiv:1710.07343},
  year   = {2017}
}

Comments

18 pages, no figures

R2 v1 2026-06-22T22:19:55.727Z