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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the singularity of random matrices with independent entries


Authors: Laurent Bruneau and François Germinet
Journal: Proc. Amer. Math. Soc. 137 (2009), 787-792
MSC (2000): Primary 15A52
Published electronically: October 22, 2008
MathSciNet review: 2457415
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Abstract: We consider $ n$ by $ n$ real matrices whose entries are non-degenerate random variables that are independent but not necessarily identically distributed, and show that the probability that such a matrix is singular is $ O(1/\sqrt{n})$. The purpose of this paper is to provide a short and elementary proof of this fact using a Bernoulli decomposition of arbitrary non-degenerate random variables.


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Additional Information

Laurent Bruneau
Affiliation: Département de Mathématiques, Université de Cergy-Pontoise, CNRS UMR 8088,F-95000 Cergy-Pontoise, France
Email: laurent.bruneau@u-cergy.fr

François Germinet
Affiliation: Département de Mathématiques, Université de Cergy-Pontoise, CNRS UMR 8088, Institut Universitaire de France, F-95000 Cergy-Pontoise, France
Email: francois.germinet@u-cergy.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09595-6
PII: S 0002-9939(08)09595-6
Received by editor(s): October 17, 2007
Published electronically: October 22, 2008
Communicated by: Walter Craig
Article copyright: © Copyright 2008 American Mathematical Society