Smallest Singular Value of a Random Rectangular Matrix
نویسندگان
چکیده
We prove an optimal estimate of the smallest singular value of a random subGaussian matrix, valid for all dimensions. For an N n matrix A with independent and identically distributed sub-Gaussian entries, the smallest singular value of A is at least of the order p N pn 1 with high probability. A sharp estimate on the probability is also obtained. © 2009 Wiley Periodicals, Inc.
منابع مشابه
The Smallest Singular Value of a Random Rectangular Matrix Mark Rudelson and Roman Vershynin
We prove an optimal estimate of the smallest singular value of a random subgaussian matrix, valid for all dimensions. For an N × 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.
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تاریخ انتشار 2009