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arXiv · 0805.3407

The least singular value of a random square matrix is O(n^{-1/2})

Mark Rudelson·Roman Vershynin
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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.

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Mark Rudelson, Roman Vershynin. 2008-05-22. The least singular value of a random square matrix is O(n^{-1/2}). https://arxiv.org/abs/0805.3407

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