Abstract:
Developing bounds for the eigenvalues of matrix polynomials is an interesting problem
which has a lot of applications. In this thesis, several known bounds for the eigenvalues of
matrix polynomials are presented. In addition, we derive new bounds for the eigenvalues
of matrix polynomials with commuting coefficients. These bounds are based on norms,
numerical radius, and spectral radius of the coefficient matrices. Various tools are used in
the derivations, such as Frobenius companion matrix, the numerical radius inequalities,
and matrix norms. In general, it is not possible to compare the sharpness of these
bounds analytically. Therefore, we compare our new bounds with each other and with
other known bounds numerically through a set of examples.
Description:
cd, no of pages 89, 31647, ماجستير رياضيات 3/2024
