The full rank condition for sparse random matrices
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 $\{0,1\}$ -matrices over the rationals. The sufficient condition is generally necessary as well.
Authors
- Amin Coja‐Oghlan (ORCID: https://orcid.org/0000-0002-7350-1418)
- Maurice Rolvien
- Noëla Müller (ORCID: https://orcid.org/0009-0004-8182-311X)
- Max Hahn‐Klimroth (ORCID: https://orcid.org/0000-0002-3995-419X)
- Joon Lee (ORCID: https://orcid.org/0000-0001-8628-9922)
- Pu Gao (ORCID: https://orcid.org/0000-0002-6363-1681)
Publication Details
- Journal
- Combinatorics Probability Computing
- Published
- 2024-09-01
- DOI
- https://doi.org/10.1017/s096354832400021x
- Citations
- 1
- Primary Topic
- Random Matrices and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.71
Funders
- Deutsche Forschungsgemeinschaft
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Natural Sciences and Engineering Research Council of Canada