Smoothed analysis of kappa(A)
Let A = ((a(ij))) be an m x m (m greater than or equal to 3) real random matrix, with independent Gaussian entries with a common variance sigma(2). Denote by M the matrix of expected values of the entries of A. For x > 0 we prove that P(kappa(A)>m.x)  0, P(kappa(A) > m.x) < (K)/(sigmax) where K is a universal constant. (C) 2003 Elsevier Inc. All rights reserved.
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