The nonnegative inverse eigenvalue problem

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

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


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.

Original languageEnglish
Pages (from-to)475-490
Number of pages16
JournalLinear Algebra and Its Applications
Issue number1-3 SPEC. ISS
StatePublished - Mar 1 2004


  • Inverse eigenvalue problem
  • Spectrum of matrix
  • Symmetric matrices


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