Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue

Al-Saafin, Doaa; Garloff, Jürgen

Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue

Files

Al-Saafin_2-125tfy98m8rbn0.pdf(357.57 KB)

Date

2020

Authors

Al-Saafin, Doaa

Garloff, Jürgen

Series

Konstanzer Schriften in Mathematik; 390

Publication type

Working Paper/Technical Report

Publication status

Published

Abstract

Let A = [a_ij] be a real symmetric matrix. If f: (0,oo) --> [0,oo) is a Bernstein function, a sufficient condition for the matrix [f(a_ij)] to have only one positive eigenvalue is presented. By using this result, new results for a symmetric matrix with exactly one positive eigenvalue, e.g., properties of its Hadamard powers, are derived.

Subject (DDC)

510 Mathematics

Keywords

Bernstein function, Hadamard power, Hadamard inverse, distance matrix, infinitely divisible matrix, conditionally negative semidefinite matrix

Cite This

ISO 690

AL-SAAFIN, Doaa, Jürgen GARLOFF, 2020. Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue. Available under: doi: 10.1515/spma-2020-0009

BibTex

@techreport{AlSaafin2020-04-03Suffi-49263,
  year={2020},
  doi={10.1515/spma-2020-0009},
  series={Konstanzer Schriften in Mathematik},
  title={Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue},
  number={390},
  author={Al-Saafin, Doaa and Garloff, Jürgen},
  note={Erschienen in: Special Matrices ; 8 (2020), 1. - S. 98-103. - de Gruyter. - eISSN 2300-7451}
}

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    <dcterms:abstract xml:lang="eng">Let A = [a&lt;sub&gt;ij&lt;/sub&gt;] be a real symmetric matrix. If f: (0,oo) --&gt; [0,oo) is a Bernstein function, a sufficient condition for the matrix [f(a&lt;sub&gt;ij&lt;/sub&gt;)] to have only one positive eigenvalue is presented. By using this result, new results for a symmetric matrix with exactly one positive eigenvalue, e.g., properties of its Hadamard powers, are derived.</dcterms:abstract>
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Comment on publication

Erschienen in: Special Matrices ; 8 (2020), 1. - S. 98-103. - de Gruyter. - eISSN 2300-7451

Bibliography of Konstanz

Yes