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: | |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2005
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172005000100006 |
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| Sumario: | 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 |
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