Tikhomirov, Konstantin Singularity of random Bernoulli matrices. (English) Zbl 1458.15023 Ann. Math. (2) 191, No. 2, 593-634 (2020). Summary: For each \(n\), let \(M_n\) be an \(n\times n\) random matrix with independent \(\pm 1\) entries. We show that \(\mathbb{P}\{M_n\text{ is singular}\}=(1/2+o_n(1))^n\), which settles an old problem. Some generalizations are considered. Cited in 22 Documents MSC: 15A18 Eigenvalues, singular values, and eigenvectors 15B52 Random matrices (algebraic aspects) Keywords:Bernoulli matrix; singularity PDF BibTeX XML Cite \textit{K. Tikhomirov}, Ann. Math. (2) 191, No. 2, 593--634 (2020; Zbl 1458.15023) Full Text: DOI arXiv OpenURL