Browsing by Author "Istkhar Ali, Mohammad Waquas Khadim"

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    Perturbation Theory and Eigenvalue Localization for Quaternionic Matrices
    (Book Rivers, 2025) Istkhar Ali, Mohammad Waquas Khadim
    "This chapter presents a comprehensive exploration of perturbation theory and eigenvalue localization for matrices over the quaternion division algebra, addressing key theoretical and computational challenges arising from their non-commutative nature. Building on recent advances in quaternionic linear algebra, we extend classical perturbation results-such as the Bauer-Fike theorem and relative eigenvalue bounds-to the quaternionic setting, with a focus on both right and left eigenvalues, which exhibit fundamentally distinct behaviors. We derive new perturbation bounds for structured quaternionic matrices (e.g., Hermitian, unitary, and skew-Hermitian), leveraging their unique spectral properties."