On the location of eigenvalues of matrix polynomials

2017/03/02 by Lê, Công-Trình, Du, Thi-Hoa-Binh, Nguyen, Tran-Duc · 2 citations
#15A18 #15A42 #65F15 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1703.00747

Abstract

A number λ∈ \mathbb C is called an \it eigenvalue of the matrix polynomial P(z) if there exists a nonzero vector x ∈ \mathbb Cⁿ 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, J. Maroulas and P. Psarrakos.

Cited by

• Generalizations of Enestrom-Kakeya Type Theorems for matrix Polynomials
• Generalization of Cauchy type theorems for matrix Polynomials

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