REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*

Let Λ= {λ1, λ2, . . . , λn} be a set of complex numbers. The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and su.cient conditions in order that Λmay be the spectrum of an entrywise nonnegative n Χ n matrix...

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Autor principal:	SOTO,RICARDO L
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2005
Materias:	symmetric nonnegative inverse eigenvalue problem
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000100006
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spelling	oai:scielo:S0716-091720050001000062005-07-06REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*SOTO,RICARDO L symmetric nonnegative inverse eigenvalue problem Let Λ= {λ1, λ2, . . . , λn} be a set of complex numbers. The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and su.cient conditions in order that Λmay be the spectrum of an entrywise nonnegative n Χ n matrix. If there exists a nonnegative matrix A with spectrum Λ we say that Λ is realized by A.If the matrix A must be symmetric we have the symmetric nonnegative inverse eigenvalue problem (SNIEP). This paper presents a simple realizability criterion by symmetric nonnegative matrices. The proof is constructive in the sense that one can explicitly construct symmetric nonnegative matrices realizing Λinfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.24 n.1 20052005-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000100006en10.4067/S0716-09172005000100006
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	symmetric nonnegative inverse eigenvalue problem
spellingShingle	symmetric nonnegative inverse eigenvalue problem SOTO,RICARDO L REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*
description	Let Λ= {λ1, λ2, . . . , λn} be a set of complex numbers. The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and su.cient conditions in order that Λmay be the spectrum of an entrywise nonnegative n Χ n matrix. If there exists a nonnegative matrix A with spectrum Λ we say that Λ is realized by A.If the matrix A must be symmetric we have the symmetric nonnegative inverse eigenvalue problem (SNIEP). This paper presents a simple realizability criterion by symmetric nonnegative matrices. The proof is constructive in the sense that one can explicitly construct symmetric nonnegative matrices realizing Λ
author	SOTO,RICARDO L
author_facet	SOTO,RICARDO L
author_sort	SOTO,RICARDO L
title	REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*
title_short	REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*
title_full	REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*
title_fullStr	REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*
title_full_unstemmed	REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*
title_sort	realizability by symmetric nonnegative matrices*
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2005
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000100006
work_keys_str_mv	AT sotoricardol realizabilitybysymmetricnonnegativematrices
_version_	1718439740647145472

REALIZABILITY BY SYMMETRIC NONNEGATIVE MATRICES*

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