On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices

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 p...

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Autores principales:	Pickmann-Soto,H., Arela Pérez,Susana, Egaña,J., Carrasco Olivera,D.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2019
Materias:	Arrow matrices Symmetric and nonsymmetric matrix Inverse eigenvalue problem.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000400811
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spelling	oai:scielo:S0716-091720190004008112019-11-04On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matricesPickmann-Soto,H.Arela Pérez,SusanaEgaña,J.Carrasco Olivera,D. Arrow matrices Symmetric and nonsymmetric matrix Inverse eigenvalue problem. 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.4 20192019-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000400811en10.22199/issn.0717-6279-2019-04-0053
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Arrow matrices Symmetric and nonsymmetric matrix Inverse eigenvalue problem.
spellingShingle	Arrow matrices Symmetric and nonsymmetric matrix Inverse eigenvalue problem. Pickmann-Soto,H. Arela Pérez,Susana Egaña,J. Carrasco Olivera,D. On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices
description	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.
author	Pickmann-Soto,H. Arela Pérez,Susana Egaña,J. Carrasco Olivera,D.
author_facet	Pickmann-Soto,H. Arela Pérez,Susana Egaña,J. Carrasco Olivera,D.
author_sort	Pickmann-Soto,H.
title	On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices
title_short	On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices
title_full	On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices
title_fullStr	On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices
title_full_unstemmed	On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices
title_sort	on the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000400811
work_keys_str_mv	AT pickmannsotoh ontheinverseeigenproblemforsymmetricandnonsymmetricarrowheadmatrices AT arelaperezsusana ontheinverseeigenproblemforsymmetricandnonsymmetricarrowheadmatrices AT eganaj ontheinverseeigenproblemforsymmetricandnonsymmetricarrowheadmatrices AT carrascooliverad ontheinverseeigenproblemforsymmetricandnonsymmetricarrowheadmatrices
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On the inverse eigenproblem for symmetric and nonsymmetric arrowhead matrices

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