The nonnegative inverse eigenvalue problem

Patricia D. Egleston; Terry D. Lenker; Sivaram K. Narayan

doi:10.1016/j.laa.2003.10.019

The nonnegative inverse eigenvalue problem

Patricia D. Egleston, Terry D. Lenker, Sivaram K. Narayan

Mathematics

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56 Scopus citations

Abstract

Let σ = (λ₁,⋯,λ_n) be a list of complex numbers. The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and sufficient conditions in order that σ be the spectrum of an entrywise nonnegative n × n matrix. Our purpose is to give an overview of the NIEP, its history, modern results, and subproblems with particular emphasis on symmetric realizing matrices. A substantial bibliography is included.

Original language	English
Pages (from-to)	475-490
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	379
Issue number	1-3 SPEC. ISS
DOIs	https://doi.org/10.1016/j.laa.2003.10.019
State	Published - Mar 1 2004

Keywords

Inverse eigenvalue problem
Spectrum of matrix
Symmetric matrices

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10.1016/j.laa.2003.10.019

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AU - Narayan, Sivaram K.

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N2 - Let σ = (λ1,⋯,λn) be a list of complex numbers. The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and sufficient conditions in order that σ be the spectrum of an entrywise nonnegative n × n matrix. Our purpose is to give an overview of the NIEP, its history, modern results, and subproblems with particular emphasis on symmetric realizing matrices. A substantial bibliography is included.

AB - Let σ = (λ1,⋯,λn) be a list of complex numbers. The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and sufficient conditions in order that σ be the spectrum of an entrywise nonnegative n × n matrix. Our purpose is to give an overview of the NIEP, its history, modern results, and subproblems with particular emphasis on symmetric realizing matrices. A substantial bibliography is included.

KW - Inverse eigenvalue problem

KW - Spectrum of matrix

KW - Symmetric matrices

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JO - Linear Algebra and Its Applications

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IS - 1-3 SPEC. ISS

ER -

The nonnegative inverse eigenvalue problem

Abstract

Keywords

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