On the product of singular symmetric matrices
نویسندگان
چکیده
منابع مشابه
On the least singular value of random symmetric matrices
Let Fn be an n by n symmetric matrix whose entries are bounded by n γ for some γ > 0. Consider a randomly perturbed matrix Mn = Fn +Xn, where Xn is a random symmetric matrix whose upper diagonal entries xij , 1 ≤ i ≤ j, are iid copies of a random variable ξ. Under a very general assumption on ξ, we show that for any B > 0 there exists A > 0 such that P(σn(Mn) ≤ n−A) ≤ n−B .
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1969-0242856-4