(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."
