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

DOI:
https://doi.org/10.1090/S0002-9939-08-09595-6

Published electronically:
October 22, 2008

MathSciNet review:
2457415

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider by 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 . 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:
https://doi.org/10.1090/S0002-9939-08-09595-6

Received by editor(s):
October 17, 2007

Published electronically:
October 22, 2008

Communicated by:
Walter Craig

Article copyright:
© Copyright 2008
American Mathematical Society