Perturbation analysis of matrices over a quaternion division algebra. ETNA - Electronic Transactions on Numerical Analysis

Autor:	Ali, Istkhar, Slapničar, Ivan, Ahmad, Sk. Safique
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	quaternionic matrices left eigenvalues right eigenvalues quaternionic polynomials Bauer-Fike theorem quaternionic companion matrices quaternionic matrix norms Mathematics Physics and Space Research Mathematics::Differential Geometry
Popis:	In this paper, we present the concept of perturbation bounds for the right eigenvalues of a quaternionic matrix. In particular, a Bauer-Fike-type theorem for the right eigenvalues of a diagonalizable quaternionic matrix is derived. In addition, perturbations of a quaternionic matrix are discussed via a block-diagonal decomposition and the Jordan canonical form of a quaternionic matrix. The location of the standard right eigenvalues of a quaternionic matrix and a sufficient condition for the stability of a perturbed quaternionic matrix are given. As an application, perturbation bounds for the zeros of quaternionic polynomials are derived. Finally, we give numerical examples to illustrate our results.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=od_______386::57c5bb5e87669aa46c2f59da35f77be8 http://epub.oeaw.ac.at/?arp=buecher/Organisationseinheiten/_id105092_/ETNA/etna_Vol_54/pp128-149.pdf Zobrazit plný text záznamu