Location and Perturbation Analysis of Quaternionic Matrix Polynomials

Abstract

Localization theorems for the right eigenvalues of quaternionic matrix polynomials are given. A Bauer–Fike–type theorem for the right eigenvalues of diagonalizable quaternionic matrices is derived using the real adjoint matrix representation. A perturbation analysis for the right eigenvalues of quaternionic matrix polynomials is presented. The condition number of a simple right eigenvalue of a scalar polynomial is obtained. Numerical examples are provided to illustrate the results.