On a strong form of a conjecture of Boyle and Handelman
نویسندگان
چکیده
منابع مشابه
An Upper Bound on the Characteristic Polynomial of a Nonnegative Matrix Leading to a Proof of the Boyle–handelman Conjecture
In their celebrated 1991 paper on the inverse eigenvalue problem for nonnegative matrices, Boyle and Handelman conjectured that if A is an (n+1)×(n+1) nonnegative matrix whose nonzero eigenvalues are: λ0 ≥ |λi|, i = 1, . . . , r, r ≤ n, then for all x ≥ λ0, (∗) r ∏ i=0 (x− λi) ≤ x − λ 0 . To date the status of this conjecture is that Ambikkumar and Drury (1997) showed that the conjecture is tru...
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The condition (1.1) on λ1, . . . , λn is a well–known necessary condition for n numbers to be the eigenvalues of an n× n nonnegative matrix (see, for example, Berman and Plemmons [3]). Furthermore, from a result due to Friedland [6, Theorem 1], it is known that (1.1) implies that one of the λi’s is nonnegative and majorizes the moduli of the remaining numbers. Assume for the moment, without los...
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