Geodesic
On Cauchy-type bounds for the eigenvalues of a special class of matrix polynomials
Ural mathematical journal, Tome 9 (2023) no. 1, pp. 113-120

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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.
Keywords: eigenvalue, positive-definite matrix, Cauchy's theorem, spectral radius.
Mots-clés : matrix polynomial 
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     title = {On {Cauchy-type} bounds for the eigenvalues of a special class of matrix polynomials},
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Zahid Bashir Monga; Wali Mohammad Shah. On Cauchy-type bounds for the eigenvalues of a special class of matrix polynomials. Ural mathematical journal, Tome 9 (2023) no. 1, pp. 113-120. http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a8/