On numerical radius inequalities for n× n operator matrices and applications to bounding the zeros of polynomials
Fuad Kıttaneh, Satyajit Sahoo · Linear and Multilinear Algebra · 2025
The main purpose of the article is to establish a numerical radius inequality for operator matrices, which improves an earlier inequality due to Hou and Du [Integral Equ. Oper. Theory 22 (1995), 281–294; MR1337376]. As an application of this inequality, we derive new bounds for the zeros of polynomials. Also, we provide some examples to illustrate our results. Finally, we obtain certain new bounds for the zeros of a class of Fibonacci-type polynomials by using various matrix analytic methods.