The Nonnegative Inverse Eigenvalue Problem

P Egleston; Sivaram Krishnan Narayan

The Nonnegative Inverse Eigenvalue Problem

Mathematics

Research output: Contribution to journal › Article › peer-review

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
Journal	Linear Algebra and Its Applications
Issue number	379
State	Published - 2004

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title = "The Nonnegative Inverse Eigenvalue Problem",

abstract = "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.",

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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.

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SP - 475

EP - 490

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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The Nonnegative Inverse Eigenvalue Problem

Abstract

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