2024/04/13 by Pallavi Basavaraju, Basavaraju, Pallavi, Shrinath Hadimani +3
Computer Science · Mathematics · Medicine · #12E15 #15A18 #15A42 #15A66 #15B33 #FOS: Mathematics #Matrix Theory and Algorithms #Ophthalmology and Eye Disorders #Point processes and geometric inequalities #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2404.08932
openalex publication_date 2024/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.