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Karami, Saeed

Numerical radius of the powers of Jordan block and its application for eigenvalue of nonnegative symmetric Toeplitz matrices. (English) Zbl 1529.15010

Appl. Math. E-Notes 23, 537-543 (2023).
Summary: In this paper, we present a formula for the numerical radius of the powers of a Jordan block. This formula gives us an analytic and simple upper bound for the maximum eigenvalues of the nonnegative symmetric Toeplitz matrices. Numerical examples are provided to evaluate the accuracy level of the obtained upper bound in comparison with some existing bounds.

MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15A20 Diagonalization, Jordan forms
15B05 Toeplitz, Cauchy, and related matrices
47A12 Numerical range, numerical radius

Keywords:

numerical radius; Jordan block; Toeplitz matrices
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References:

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