On the singularity of random matrices with independent entries
Authors:
Laurent Bruneau and François Germinet
Journal:
Proc. Amer. Math. Soc. 137 (2009), 787792
MSC (2000):
Primary 15A52
Published electronically:
October 22, 2008
MathSciNet review:
2457415
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Abstract: We consider by real matrices whose entries are nondegenerate 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 nondegenerate random variables.
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Additional Information
Laurent Bruneau
Affiliation:
Département de Mathématiques, Université de CergyPontoise, CNRS UMR 8088,F95000 CergyPontoise, France
Email:
laurent.bruneau@ucergy.fr
François Germinet
Affiliation:
Département de Mathématiques, Université de CergyPontoise, CNRS UMR 8088, Institut Universitaire de France, F95000 CergyPontoise, France
Email:
francois.germinet@ucergy.fr
DOI:
http://dx.doi.org/10.1090/S0002993908095956
PII:
S 00029939(08)095956
Received by editor(s):
October 17, 2007
Published electronically:
October 22, 2008
Communicated by:
Walter Craig
Article copyright:
© Copyright 2008
American Mathematical Society
