Computation of the zeros of a quaternionic polynomial using matrix methods
AbstractIn a recent paper, Ishfaq Dar (2024), worked on the problem of locating the zeros of quaternion polynomials by introducing various matrix techniques. In this paper, we use those newly developed matrix methods to locate the left eigenvalues of the quaternion companion matrix of the polynomial...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2024-12-01
|
| Series: | Arab Journal of Basic and Applied Sciences |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2023.2301237 |
| _version_ | 1797361786182172672 |
|---|---|
| author | N. A. Rather Tanveer Bhat Ishfaq Dar Bilal Khan Arjika Sama |
| author_facet | N. A. Rather Tanveer Bhat Ishfaq Dar Bilal Khan Arjika Sama |
| author_sort | N. A. Rather |
| collection | DOAJ |
| description | AbstractIn a recent paper, Ishfaq Dar (2024), worked on the problem of locating the zeros of quaternion polynomials by introducing various matrix techniques. In this paper, we use those newly developed matrix methods to locate the left eigenvalues of the quaternion companion matrix of the polynomial, which in turn yield various results concerning the location of the zeros of quaternionic polynomials including extensions of the results of Rubinstein and A. Aziz to the quaternionic setting as well. |
| first_indexed | 2024-03-08T15:59:24Z |
| format | Article |
| id | doaj.art-42cd972f465a44159b9d72400d31cf12 |
| institution | Directory Open Access Journal |
| issn | 2576-5299 |
| language | English |
| last_indexed | 2024-03-08T15:59:24Z |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj.art-42cd972f465a44159b9d72400d31cf122024-01-08T12:03:48ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992024-12-01311657010.1080/25765299.2023.2301237Computation of the zeros of a quaternionic polynomial using matrix methodsN. A. Rather0Tanveer Bhat1Ishfaq Dar2Bilal Khan3Arjika Sama4Department of Mathematics, University of Kashmir, Srinagar, IndiaDepartment of Mathematics, University of Kashmir, Srinagar, IndiaDepartment of Applied Sciences, Institute of Technology, University of Kashmir, Srinagar, IndiaSchool of Mathematical Sciences and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, ChinaDepartment of Mathematics and Informatics, University of Agadez, Agadez, NigerAbstractIn a recent paper, Ishfaq Dar (2024), worked on the problem of locating the zeros of quaternion polynomials by introducing various matrix techniques. In this paper, we use those newly developed matrix methods to locate the left eigenvalues of the quaternion companion matrix of the polynomial, which in turn yield various results concerning the location of the zeros of quaternionic polynomials including extensions of the results of Rubinstein and A. Aziz to the quaternionic setting as well.https://www.tandfonline.com/doi/10.1080/25765299.2023.2301237Companion matrixquaternionic polynomialsright (and left) quaternionic eigenvalues30A1030C1030C15 |
| spellingShingle | N. A. Rather Tanveer Bhat Ishfaq Dar Bilal Khan Arjika Sama Computation of the zeros of a quaternionic polynomial using matrix methods Arab Journal of Basic and Applied Sciences Companion matrix quaternionic polynomials right (and left) quaternionic eigenvalues 30A10 30C10 30C15 |
| title | Computation of the zeros of a quaternionic polynomial using matrix methods |
| title_full | Computation of the zeros of a quaternionic polynomial using matrix methods |
| title_fullStr | Computation of the zeros of a quaternionic polynomial using matrix methods |
| title_full_unstemmed | Computation of the zeros of a quaternionic polynomial using matrix methods |
| title_short | Computation of the zeros of a quaternionic polynomial using matrix methods |
| title_sort | computation of the zeros of a quaternionic polynomial using matrix methods |
| topic | Companion matrix quaternionic polynomials right (and left) quaternionic eigenvalues 30A10 30C10 30C15 |
| url | https://www.tandfonline.com/doi/10.1080/25765299.2023.2301237 |
| work_keys_str_mv | AT narather computationofthezerosofaquaternionicpolynomialusingmatrixmethods AT tanveerbhat computationofthezerosofaquaternionicpolynomialusingmatrixmethods AT ishfaqdar computationofthezerosofaquaternionicpolynomialusingmatrixmethods AT bilalkhan computationofthezerosofaquaternionicpolynomialusingmatrixmethods AT arjikasama computationofthezerosofaquaternionicpolynomialusingmatrixmethods |