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Smallest singular value of sparse random matrices. (English) Zbl 1277.60016

The authors prove nonasymptotic bounds on the smallest singular value of rectangular random matrices with independent, not necessarily identically distributed, centered entries, under moment conditions and the requirement that the upper tail of the norm of a matrix decay exponentially. In contrast to previous joint articles of the first author with Pajor, Tomczak-Jaegermann and various other authors, it is not required that individual entries satisfy lower bounds on their variances (instead, one has lower bounds on the variances of columns), thus extending previous results to sparse random matrices.

MSC:

60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
46B06 Asymptotic theory of Banach spaces
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