Characteristic polynomials of symmetric matrices
نویسندگان
چکیده
منابع مشابه
Characteristic polynomials of real symmetric random matrices
It is shown that the correlation functions of the random variables det(λ−X), in which X is a real symmetric N × N random matrix, exhibit universal local statistics in the large N limit. The derivation relies on an exact dual representation of the problem: the k-point functions are expressed in terms of finite integrals over (quaternionic) k × k matrices. However the control of the Dyson limit, ...
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Let f(x) ∈ Z[x] be a totally real polynomial with roots α1 ≤ . . . ≤ αd. The span of f(x) is defined to be αd − α1. Monic irreducible f(x) of span less than 4 are special. In this paper we give a complete classification of those small-span polynomials which arise as characteristic polynomials of integer symmetric matrices. As one application, we find some low-degree polynomials that do not aris...
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An oriented graph Gσ is a simple undirected graph G with an orientation, which assigns to each edge a direction so that Gσ becomes a directed graph. G is called the underlying graph of Gσ and we denote by S(Gσ) the skew-adjacency matrix of Gσ and its spectrum Sp(Gσ) is called the skew-spectrum of Gσ. In this paper, the coefficients of the characteristic polynomial of the skew-adjacency matrix S...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1968
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1968.25.433