A family of realizability criteria for the real and symmetric nonnegative inverse eigenvalue problem

SUMMARYA new realizability criterion for the real nonnegative inverse eigenvalue problemis 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 matrixwith 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.