DOI:  http://dx.doi.org/10.18273/revint.v35n1-2017003

Original article

A recursive condition for the symmetric nonnegative inverse  eigenvalue  problema

Una condición recursiva para el problema inverso del autovalor para matrices  simétricas no negativas

 

ELVIS RONALD VALERO¹

EXEQUIEL MALLEA-ZEPEDA¹

EBER LENES²

 

¹Universidad de Tarapacá, Departamento de Matemática, Arica, Chile.

²Universidad del Sinú. Elías Bechara Zainum, Departamento de Matemática, Cartagena, Colombia

 

E-mail: evalero@uta.cl 

 

Abstract:

In this paper we present a sufficient condition and a  necessary condition for Symmetric Nonnegative Inverse Eigenvalue Problem. This condition is independent of the existing realizability criteria. This  Criterion is recursive, that is, it determines whether a list A = {Al, ... , An, An+d is realizable by a nonnegative symmetric matrix, if the list M = {MI, ... , Mn} associated to A is realizable. This result is easy to program and improves sorne existing criteria.

Keywords: Inverse problems, eigenvalues, orthogonal matrices, symmetric matrix.

 

Resumen:

En este artículo presentamos una condición suficiente y una condición necesaria para el Problema Inverso de Autovalores para Matrices  Simétricas no Negativas. Esta condición es independiente de los criterios de realizabilidad existentes. Este criterio es recursivo, es decir determina si una lista A = {Al, ... , An, An+d es realizable por una matriz simétrica no negativa, si la lista M = {MI, ... , Mn} asociada a A es realizable. Este resultado es fácil de programar y mejora algunos criterios existentes.

Palabras clave: Problemas inversos, autovalores, matrices ortogonales, matrices simétricas.

 

Received: 9 March 2017,

Accepted: 24 May 2017.

 

Texto completo disponible en PDF

 

 

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To cite this article: E.R. Valero, E. Mallea-Zepeda, E. Lenes, A recursive condition for the symmetric nonnegative inverse eigenvalue problem, Rev. Integr. Temas Mat. 35 (2017), No. 1,37- 50.