A family of realizability criteria for the real and symmetric nonnegative inverse eigenvalue problem1. Issue 2 (13th December 2011)

• Record Type: Journal Article
• Authors: Soto, Ricardo L.
• Other Names: Chu Eric guestEditor.; Lin Wen‐wei guestEditor.; Reichel Lothar guestEditor.
• Is Part Of: Numerical linear algebra with applications. Volume 20:Issue 2(2013:Mar.)
• Page Start: 336
• Page End: 348
• Publication Date: 2011-12-13
• Subjects: real and symmetric nonnegative inverse eigenvalue problem; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.835
• Languages: English
• ISSNs: 1070-5325

Abstract

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.