A study of the validity of Oppenheim's inequality for Hurwitz matrices associated with Hurwitz polynomials
- 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 the Hurwitz matrices up to order 6, and (iii) a necessary and sufficient condition for the Hadamard square root of Hurwitz polynomials of degree five to be Hurwitz.
| Author: | Fatimah AlsaafinORCiD, Doaa Al-SaafinORCiD, Jürgen GarloffORCiDGND |
|---|---|
| URN: | urn:nbn:de:bsz:352-2-1tjehyszje6it1 |
| DOI: | https://doi.org/10.13001/ela.2024.8371 |
| ISSN: | 1537-9582 |
| eISSN: | 1081-3810 |
| Parent Title (English): | Electronic Journal of Linear Algebra (ELA) |
| Volume: | Vol. 40 |
| Publisher: | International Linear Algebra Society (ILAS) |
| Document Type: | Article |
| Language: | English |
| Year of Publication: | 2024 |
| Release Date: | 2024/12/02 |
| Tag: | Hurwitz polynomial; Hurwitz matrix; Hadamard product; Oppenheim's inequality |
| First Page: | 574 |
| Last Page: | 584 |
| Institutes: | Institut für Angewandte Forschung - IAF |
| DDC functional group: | 510 Mathematik |
| Open Access?: | Ja |
| Relevance: | Wiss. Zeitschriftenartikel reviewed: Listung in Positivlisten |
| Licence (German): |  Urheberrechtlich geschützt |
