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On coneigenvalues of quaternion matrices: location and perturbation

Author

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  • Pallavi Basavaraju

    (Dr. G. Shankar Government Women’s First Grade College and P.G Study Centre)

  • Shrinath Hadimani

    (Manipal Institute of Technology, MAHE)

  • Sachindranath Jayaraman

    (Indian Institute of Science Education and Research Thiruvananthapuram)

Abstract

We derive some localization and perturbation results for coneigenvalues of quaternion matrices. In localization results, we derive Geršgorin type theorems for right and left coneigenvalues of quaternion matrices. We prove that certain coneigenvalues lie in the union of Geršgorin balls, in contrast to the complex situation where all eigenvalues lie in the union of Geršgorin discs. In perturbation results, we derive a result analogous to the Hoffman-Wielandt inequality for basal right coneigenvalues of conjugate normal quaternion matrices. Results analogous to the Bauer-Fike theorem and a generalization of the Hoffman-Wielandt inequality are discussed for basal right coneigenvalues of condiagonalizable quaternion matrices. Finally, we define spectral variation and Hausdorff distance between right (con)eigenvalues of two quaternion matrices and obtain bounds on them.

Suggested Citation

  • Pallavi Basavaraju & Shrinath Hadimani & Sachindranath Jayaraman, 2025. "On coneigenvalues of quaternion matrices: location and perturbation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(3), pages 1144-1155, September.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:3:d:10.1007_s13226-025-00829-y
    DOI: 10.1007/s13226-025-00829-y
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