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

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

2008-05-22

arxiv.org/abs/0805.3407v1

Mathematics

Probability

6 pages

Scientific paper

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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