Various 3 × 3 nonnegative matrices with prescribed eigenvalues and diagonal entries

Jin Ok Hwang, Donggyun Kim

Research output: Contribution to journalArticlepeer-review


In this paper, we answer the various forms of nonnegative inverse eigenvalue problems with prescribed diagonal entries for order three: real or complex general matrices, symmetric stochastic matrices, and real or complex doubly stochastic matrices. We include the known cases, the symmetric matrices and real or complex stochastic matrices, to compare the other results and for completeness. In addition, for a given list of eigenvalues, we compute the exact range for the largest value of the diagonal entries of the various nonnegative matrices.

Original languageEnglish
Pages (from-to)15-48
Number of pages34
JournalLinear Algebra and Its Applications
Publication statusPublished - 2018 Oct 1

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.


  • Doubly stochastic matrices
  • Nonnegative inverse eigenvalue problems
  • Nonnegative matrices
  • Stochastic matrices
  • Symmetric matrices
  • Symmetric stochastic matrices

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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