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

Jin Ok Hwang, Donggyun Kim

Research output: Contribution to journalArticle

Abstract

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
Volume554
DOIs
Publication statusPublished - 2018 Oct 1

Fingerprint

Nonnegative Matrices
Stochastic Matrix
Eigenvalue
Symmetric matrix
Doubly Stochastic Matrix
Inverse Eigenvalue Problem
Completeness
Non-negative
Range of data

Keywords

  • 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

Cite this

Various 3 × 3 nonnegative matrices with prescribed eigenvalues and diagonal entries. / Hwang, Jin Ok; Kim, Donggyun.

In: Linear Algebra and Its Applications, Vol. 554, 01.10.2018, p. 15-48.

Research output: Contribution to journalArticle

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