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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.4 Antofagasta dic. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-04-0053 

Articles

On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices

1Universidad de Tarapacá, Dept. de Matemática, Arica, Chile. e-mail: hpickmanns@academicos.uta.cl

2Universidad de Tarapacá, Dept. de Matemática, Arica, Chile, e-mail: susana.arela.p@gmail.com

3Universidad Católica del Norte, Dept. de Matemáticas, Antofagasta, Chile, e-mail: jegana@ucn.cl

4Universidad del Bío-Bío, Dept de Matemática, Concepción, Chile, e-mail : dcarrasc@ubiobio.cl

Abstract

We present a new construction of a symmetric arrow matrix from a particular spectral information: let λ(n) 1 be the minimal eigenvalue of the matrix and λj (j) , j = 1, 2, . . . , n the maximal eigenvalues of all leading principal submatrices of the matrix. We use such a procedure to construct a nonsymmetric arrow matrix from the same spectral information plus to an eigenvector x(n) = (x1, x2, . . . , xn), so that (x(n), λn (n)) is an eigenpair of the matrix. Moreover, our results generate an algorithmic procedure to compute a solution matrix.

Keywords: Arrow matrices; Symmetric and nonsymmetric matrix; Inverse eigenvalue problem.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgement

We thank Professor Hector Miranda for suggestions and comments to improve this article.

Supported by Proyecto Mayor de Investigación Científica y Tecnológica UTA 4747-19

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Received: May 2019; Accepted: June 2019

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