Naslov
Perturbation analysis of matrices over a quaternion division algebra

Autori
Ahmad, Sk. Safique ; Ali, Istkhar ; Slapničar, Ivan

Izvornik
Electronic Transactions on Numerical Analysis (1068-9613) 54 (2021); 128-149

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
quaternionic matrices ; left eigenvalues ; right eigenvalues ; quaternionic polynomials ; Bauer-Fike theorem ; quaternionic companion matrices ; quaternionic matrix norms

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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