Publikation: Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue
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2020
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Zusammenfassung
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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Fachgebiet (DDC)
510 Mathematik
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Bernstein function, Hadamard power, Hadamard inverse, distance matrix, infinitely divisible matrix, conditionally negative semidefinite matrix
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AL-SAAFIN, Doaa, Jürgen GARLOFF, 2020. Sufficient conditions for symmetric matrices to have exactly one positive eigenvalueBibTex
@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<sub>ij</sub>] be a real symmetric matrix. If f: (0,oo) --> [0,oo) is a Bernstein function, a sufficient condition for the matrix [f(a<sub>ij</sub>)] 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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