This is an announcement for the paper "The least singular value of a random square matrix is O(n^{-1/2})" by Mark Rudelson and Roman Vershynin.
Abstract: Let A be a matrix whose entries are real i.i.d. centered random variables with unit variance and suitable moment assumptions. Then the smallest singular value of A is of order n^{-1/2} with high probability. The lower estimate of this type was proved recently by the authors; in this note we establish the matching upper estimate.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 15A52
Remarks: 6 pages
The source file(s), square-matrices-reverse.tex: 17210 bytes, is(are) stored in gzipped form as 0805.3407.gz with size 6kb. The corresponding postcript file has gzipped size 68kb.
Submitted from: vershynin@math.ucdavis.edu
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