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Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue

Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue

Type of Publication: Working Paper/Technical Report
Publication status: Published
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-2-125tfy98m8rbn0
Author: Al-Saafin, Doaa; Garloff, Jürgen
Year of publication: 2020
Series: Konstanzer Schriften in Mathematik ; 390
DOI (citable link): https://dx.doi.org/10.1515/spma-2020-0009
Summary:
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.
Subject (DDC): 510 Mathematics
Keywords: Bernstein function, Hadamard power, Hadamard inverse, distance matrix, infinitely divisible matrix, conditionally negative semidefinite matrix
Comment on publication: Erschienen in: Special Matrices ; 8 (2020), 1. - S. 98-103. - de Gruyter. - eISSN 2300-7451
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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

@techreport{AlSaafin2020-04-03Suffi-49263, series={Konstanzer Schriften in Mathematik}, title={Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue}, year={2020}, doi={10.1515/spma-2020-0009}, 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} }

Al-Saafin, Doaa 2020-04-03 eng 2020-04-23T07:57:12Z Garloff, Jürgen 2020-04-23T07:57:12Z Al-Saafin, Doaa Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue 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. Garloff, Jürgen

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