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arXiv · 0802.3956

The smallest singular value of a random rectangular matrix

Mark Rudelson·Roman Vershynin
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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.

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Mark Rudelson, Roman Vershynin. 2008-02-27. The smallest singular value of a random rectangular matrix. https://arxiv.org/abs/0802.3956

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