The smallest singular value of a random rectangular matrix

Details The smallest singular value of a random rectangular matrix The smallest singular value of a random rectangular matrix

2008-02-27

arxiv.org/abs/0802.3956v4

Mathematics

Probability

33 pages. A few misprints corrected

Scientific paper

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.

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