English

The full rank condition for sparse random matrices

Combinatorics 2022-02-08 v2 Discrete Mathematics Probability

Abstract

We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. The result covers both matrices over finite fields with independent non-zero entries and {0,1}\{0,1\}-matrices over the rationals. The sufficient condition is generally necessary as well.

Keywords

Cite

@article{arxiv.2112.14090,
  title  = {The full rank condition for sparse random matrices},
  author = {Amin Coja-Oghlan and Pu Gao and Max Hahn-Klimroth and Joon Lee and Noela Müller and Maurice Rolvien},
  journal= {arXiv preprint arXiv:2112.14090},
  year   = {2022}
}

Comments

46 pages, 3 figures

R2 v1 2026-06-24T08:33:32.099Z