This is an announcement for the paper "The smallest singular value of a random rectangular matrix" by Mark Rudelson and Roman Vershynin.

Abstract: We prove an optimal estimate on the smallest singular value of a random subgaussian matrix, valid for all fixed dimensions. For an N by n matrix A with independent and identically distributed subgaussian entries, the smallest singular value of A is at least of the order \sqrt{N} - \sqrt{n-1} with high probability. A sharp estimate on the probability is also obtained.

Archive classification: math.PR math.FA

Mathematics Subject Classification: 15A52, 11P70

Remarks: 32 pages

The source file(s), rv-rectangular-matrices.tex: 80875 bytes, is(are) stored in gzipped form as 0802.3956.gz with size 23kb. The corresponding postcript file has gzipped size 149kb.

Submitted from: rudelson@math.missouri.edu

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http://front.math.ucdavis.edu/0802.3956

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http://arXiv.org/abs/0802.3956

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