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THE SMALLEST SINGULAR VALUE OF A RANDOM RECTANGULAR MATRIX
"... Abstract. We prove an optimal estimate on the smallest singular value of a random subgaussian matrix, valid for all fixed 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 ..."
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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 × 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. 1.