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Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue

  • 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.

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Author:Doaa Al-Saafin, Jürgen GarloffORCiDGND
Parent Title (English):Special Matrices
Document Type:Article
Year of Publication:2020
Release Date:2021/01/08
Tag:Bernstein function; Conditionally negative semidefinite matrix; Hadamard inverse; Hadamard power; Infinitely divisible matrix
First Page:98
Last Page:103
DDC functional group:500 Naturwissenschaften und Mathematik
Open Access?:Ja
Relevance:Peer reviewed Publikation in Master Journal List
Licence (German):License LogoLizenzbedingungen De Gruyter
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International