On coneigenvalues of quaternion matrices: location and perturbation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910494968774656 |
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| author | Basavaraju, Pallavi Hadimani, Shrinath Jayaraman, Sachindranath |
| author_facet | Basavaraju, Pallavi Hadimani, Shrinath Jayaraman, Sachindranath |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_08932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On coneigenvalues of quaternion matrices: location and perturbation Basavaraju, Pallavi Hadimani, Shrinath Jayaraman, Sachindranath Spectral Theory 15B33, 12E15, 15A18, 15A42, 15A66 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. |
| title | On coneigenvalues of quaternion matrices: location and perturbation |
| topic | Spectral Theory 15B33, 12E15, 15A18, 15A42, 15A66 |
| url | https://arxiv.org/abs/2404.08932 |