Publikation:

A Study of the Validity of Oppenheim's Inequality for Hurwitz Matrices Associated with Hurwitz Polynomials

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2024

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http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1tjehyszje6it1
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https://doi.org/10.13001/ela.2024.8371
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Electronic Journal of Linear Algebra. International Linear Algebra Society (ILAS). 2024, 40, S. 574-584. ISSN 1537-9582. eISSN 1081-3810. Verfügbar unter: doi: 10.13001/ela.2024.8371

Zusammenfassung

In this paper, Hurwitz polynomials, i.e., real polynomials whose roots are located in the open left half of the complex plane, and their associated Hurwitz matrices are considered. New formulae for the principal minors of Hurwitz matrices are presented which lead to (i) a new criterion for deciding whether a polynomial is Hurwitz, (ii) an inequality of a type of Oppenheim's inequality for Hurwitz matrices up to order six, and (iii) a necessary and sufficient condition for the Hadamard square root of Hurwitz polynomials of degree five to be Hurwitz.

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Fachgebiet (DDC)
510 Mathematik

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Hurwitz polynomial, Hurwitz matrix, Hadamard product, Oppenheim's inequality

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ISO 690ALSAAFIN, Fatimah, Doaa AL-SAAFIN, Jürgen GARLOFF, 2024. A Study of the Validity of Oppenheim's Inequality for Hurwitz Matrices Associated with Hurwitz Polynomials. In: Electronic Journal of Linear Algebra. International Linear Algebra Society (ILAS). 2024, 40, S. 574-584. ISSN 1537-9582. eISSN 1081-3810. Verfügbar unter: doi: 10.13001/ela.2024.8371
BibTex
@article{AlSaafin2024-08Study-70646,
  year={2024},
  doi={10.13001/ela.2024.8371},
  title={A Study of the Validity of Oppenheim's Inequality for Hurwitz Matrices Associated with Hurwitz Polynomials},
  volume={40},
  issn={1537-9582},
  journal={Electronic Journal of Linear Algebra},
  pages={574--584},
  author={AlSaafin, Fatimah and Al-Saafin, Doaa and Garloff, Jürgen}
}
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