Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue

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2020
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Konstanzer Schriften in Mathematik; 390
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Abstract
Let A = [aij] be a real symmetric matrix. If f: (0,oo) --> [0,oo) is a Bernstein function, a sufficient condition for the matrix [f(aij)] 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.
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510 Mathematics
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Bernstein function, Hadamard power, Hadamard inverse, distance matrix, infinitely divisible matrix, conditionally negative semidefinite matrix
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ISO 690AL-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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Erschienen in: Special Matrices ; 8 (2020), 1. - S. 98-103. - de Gruyter. - eISSN 2300-7451
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