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 -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