Scholarlink

<p>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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On coneigenvalues of quaternion matrices: location and perturbation

  • 期刊论文

  • 发表日期：

    2025年7月11日

查看全文
  • Pallavi Basavaraju,
  • Shrinath Hadimani,
  • Sachindranath Jayaraman

摘要

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.