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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3407 or http://arXiv.org/abs/0805.3407 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3407 or in gzipped form by using subject line get 0805.3407 to: math@arXiv.org.