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Location of Right Eigenvalues of Quaternionic Matrix Polynomials

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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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Acknowledgements

This paper is fully supported by the National Science Foundation under the project “Optimization of parameter dependent mechanical systems” (IP-2014-09-9540), Grant nr. 9540.

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Authors and Affiliations

  1. Department of Mathematics, J. J. Strossmayer University of Osijek, Trg Ljudevita Gaja 6, HR-31000, Osijek, Croatia

    Istkhar Ali & Ninoslav Truhar

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  1. Istkhar Ali
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  2. Ninoslav Truhar
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Correspondence to Istkhar Ali.

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Communicated by Swanhild Bernstein.

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Ali, I., Truhar, N. Location of Right Eigenvalues of Quaternionic Matrix Polynomials. Adv. Appl. Clifford Algebras 29, 80 (2019). https://doi.org/10.1007/s00006-019-0998-4

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  • DOI: https://doi.org/10.1007/s00006-019-0998-4

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