On coneigenvalues of quaternion matrices: location and perturbation

Pallavi Basavaraju (), Shrinath Hadimani () and Sachindranath Jayaraman ()
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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

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1144-1155

Abstract: 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.

Keywords: Quaternion matrices; Standard eigenvalues of quaternion matrices; Basal right coneigenvalues; The Geršgorin theorem; The Hoffman-Wielandt and generalized Hoffman-Wielandt type inequalities; Spectral variation; Hausdorff distance between basal right coneigenvalues; 15B33; 12E15; 15A18; 15A42; 15A66 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00829-y

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