Abstract
In this paper, inclusion regions for the right eigenvalues of a quaternionic matrix polynomial are derived from Ostrowski’s type theorem for quaternionic block companion matrices. Furthermore, a right spectral radius inequality and its applications for finding bounds for the right eigenvalues of a quaternionic matrix polynomial is presented. Consequently, these bounds give bounds for the zeros of quaternionic polynomials. Finally, bounds on the eigenvalues of complex matrix polynomials are derived. The comparison between the new bounds and some existing bounds have been illustrated with several examples.
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