A family of realizability criteria for the real and symmetric nonnegative inverse eigenvalue problem1. Issue 2 (13th December 2011) - Soto, Ricardo L.
SUMMARY: A new realizability criterion for the real nonnegative inverse eigenvalue problem is introduced. This criterion is a nontrivial extension of a powerful previous sufficient condition, based on negativity compensation . If the criterion is satisfied, then we can always construct a realizing matrix. It is also proved that this new criterion is easily adaptable to be sufficient for the construction of a symmetric nonnegative matrix with given spectrum. In a natural way, the criterion extends to a family of sufficient conditions for the problem to have a solution. Copyright © 2011 John Wiley & Sons, Ltd.