Key points are not available for this paper at this time.
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 N - n-1 with high probability. A sharp estimate on the probability is also obtained.
Rudelson et al. (Wed,) studied this question.