On The Location of Eigenvalues of Matrix Polynomials
On The Location of Eigenvalues of Matrix Polynomials
Source title:
Operators and Matrices, 13(4): 937-954,
2019
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
A number is called an eigenvalue of the matrix polynomial P(z) if there exists a nonzero vector
such that P(λ)x = 0. Note that each finite eigenvalue of P(z) is a zero of the characteristic polynomial det(P(z)). In this paper we establish some (upper and lower) bounds for eigenvalues of matrix polynomials based on the norm of their coefficient matrices and compare these bounds to those given by N. J. Higham and F. Tisseur [8], J. Maroulas and P. Psarrakos [12].