In the present paper, we establish bounds for the sum of the moduli of right eigenvalues of a quaternionic matrix. As a consequence, we establish bounds for the right spectral radius of a quaternionic matrix. We also present a minimal ball in 4D spaces that contains all Geršgorin balls of a quaternionic matrix. As an application, we introduce the estimation for the right eigenvalues of quaternionic matrices in the minimal ball. Finally, we suggest some numerical examples to illustrate our results.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 6, pp. 723–735, June, 2020. Ukrainian DOI: 10.37863/umzh.v72i6.6018.
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Ali, I. Bounds for the Right Spectral Radius of Quaternionic Matrices. Ukr Math J 72, 837–852 (2020). https://doi.org/10.1007/s11253-020-01827-5
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DOI: https://doi.org/10.1007/s11253-020-01827-5