ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS

Zahid Bashir Monga     (Department of Mathematics, Central University of Kashmir, Ganderbal-191201, India)
Wali Mohammad Shah     (Department of Mathematics, Central University of Kashmir, Ganderbal-191201, India)

Abstract


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


Matrix polynomial, Eigenvalue, Positive-definite matrix, Cauchy’s theorem, Spectral radius.

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References


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DOI: http://dx.doi.org/10.15826/umj.2023.1.009

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