Realizability by symmetric nonnegative matrices

Ricardo Lorenzo Soto Montero

Resumen


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


Palabras clave


Symmetric nonnegative inverse eigenvalue problem.

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172005000100006

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