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

Jin Ok Hwang; Donggyun Kim

doi:10.1016/j.laa.2018.05.002

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

Jin Ok Hwang, Donggyun Kim

Department of Mathematics

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

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 language	English
Pages (from-to)	15-48
Number of pages	34
Journal	Linear Algebra and Its Applications
Volume	554
DOIs	https://doi.org/10.1016/j.laa.2018.05.002
Publication status	Published - 2018 Oct 1

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

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10.1016/j.laa.2018.05.002

Cite this

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title = "Various 3 × 3 nonnegative matrices with prescribed eigenvalues and diagonal entries",

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.",

keywords = "Doubly stochastic matrices, Nonnegative inverse eigenvalue problems, Nonnegative matrices, Stochastic matrices, Symmetric matrices, Symmetric stochastic matrices",

author = "Hwang, {Jin Ok} and Donggyun Kim",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

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doi = "10.1016/j.laa.2018.05.002",

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AU - Hwang, Jin Ok

AU - Kim, Donggyun

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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.

AB - 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.

KW - Doubly stochastic matrices

KW - Nonnegative inverse eigenvalue problems

KW - Nonnegative matrices

KW - Stochastic matrices

KW - Symmetric matrices

KW - Symmetric stochastic matrices

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DO - 10.1016/j.laa.2018.05.002

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SN - 0024-3795

VL - 554

SP - 15

EP - 48

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this

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