An upper bound on the characteristic polynomial of a nonnegative matrix leading to a proof of the Boyle-Handelman conjecture
Assaf Goldberger, Michael Neumann · Proceedings of the American Mathematical Society · 2009
In their celebrated 1991 paper on the inverse eigenvalue problem for nonnegative matrices, Boyle and Handelman conjectured that if A A is an ( n + 1 ) × ( n + 1 ) (n+1)\times (n+1) nonnegative matrix whose nonzero eigenvalues are: λ 0 ≥ | λ i | \lambda _0 \geq |\lambda _i| , i = 1 , … , r i=1,\ldots ,r , r ≤ n r \leq \ n , then for all x ≥ λ 0 x \geq \lambda _0 , ( ∗ ) ∏ i = 0 r ( x − λ i ) ≤ x r + 1 − λ 0