On the Calculation of Eigenvalues and Eigenvectors of Matrix Polynomials and Orthogonality Relations between their Eigenvectors

Abstract

In the paper, the computation of the eigenvalues and eigenvectors of polynomial eigenvalue problem via standard eigenvalue problems is presented. We also establish orthogonality relations between the eigenvectors of matrix polynomials. A numerical example is given to illustrate the applicability of the obtained theoretical results.