ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS
Let \(\mathbb{C}^{m\times m}\) be the set of all \(m\times m\) matrices whose entries are in \(\mathbb{C},\) the set of complex numbers. Then \(P(z):=\sum\limits_{j=0}^nA_jz^j,\) \(A_j\in \mathbb{C}^{m\times m},\) \(0\leq j\leq n\) is called a matrix polynomial. If \(A_{n}\neq 0\), then \(P(z)\) is...
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2023-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/530 |
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| author | Zahid Bashir Monga Wali Mohammad Shah |
| author_facet | Zahid Bashir Monga Wali Mohammad Shah |
| author_sort | Zahid Bashir Monga |
| collection | DOAJ |
| description | Let \(\mathbb{C}^{m\times m}\) be the set of all \(m\times m\) matrices whose entries are in \(\mathbb{C},\) the set of complex numbers. Then \(P(z):=\sum\limits_{j=0}^nA_jz^j,\) \(A_j\in \mathbb{C}^{m\times m},\) \(0\leq j\leq n\) is called a matrix polynomial. If \(A_{n}\neq 0\), then \(P(z)\) is said to be a matrix polynomial of degree \(n\). In this paper we prove some results for the bound estimates of the eigenvalues of some lacunary type of matrix polynomials. |
| format | Article |
| id | doaj-art-5f1724bdc3ea4d6aafaf32d93f596751 |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-5f1724bdc3ea4d6aafaf32d93f5967512025-08-20T03:33:03ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522023-07-019110.15826/umj.2023.1.009173ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALSZahid Bashir Monga0Wali Mohammad Shah1Department of Mathematics, Central University of Kashmir, Ganderbal-191201Department of Mathematics, Central University of Kashmir, Ganderbal-191201Let \(\mathbb{C}^{m\times m}\) be the set of all \(m\times m\) matrices whose entries are in \(\mathbb{C},\) the set of complex numbers. Then \(P(z):=\sum\limits_{j=0}^nA_jz^j,\) \(A_j\in \mathbb{C}^{m\times m},\) \(0\leq j\leq n\) is called a matrix polynomial. If \(A_{n}\neq 0\), then \(P(z)\) is said to be a matrix polynomial of degree \(n\). In this paper we prove some results for the bound estimates of the eigenvalues of some lacunary type of matrix polynomials.https://umjuran.ru/index.php/umj/article/view/530matrix polynomial, eigenvalue, positive-definite matrix, cauchy’s theorem, spectral radius. |
| spellingShingle | Zahid Bashir Monga Wali Mohammad Shah ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS Ural Mathematical Journal matrix polynomial, eigenvalue, positive-definite matrix, cauchy’s theorem, spectral radius. |
| title | ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS |
| title_full | ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS |
| title_fullStr | ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS |
| title_full_unstemmed | ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS |
| title_short | ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS |
| title_sort | on cauchy type bounds for the eigenvalues of a special class of matrix polynomials |
| topic | matrix polynomial, eigenvalue, positive-definite matrix, cauchy’s theorem, spectral radius. |
| url | https://umjuran.ru/index.php/umj/article/view/530 |
| work_keys_str_mv | AT zahidbashirmonga oncauchytypeboundsfortheeigenvaluesofaspecialclassofmatrixpolynomials AT walimohammadshah oncauchytypeboundsfortheeigenvaluesofaspecialclassofmatrixpolynomials |