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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3956 or http://arXiv.org/abs/0802.3956 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3956 or in gzipped form by using subject line get 0802.3956 to: math@arXiv.org.