An alternative canonical form for quaternionic H-unitary matrices

G. J. Groenewald, D. B. Janse van Rensburg, A. C.M. Ran*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

The field of linear algebra over the quaternions is a research area which is still in development. In this paper we continue our research on canonical forms for a matrix pair (A,H), where the matrix A is H-unitary, H is invertible and with A as well as H quaternionic matrices. We seek an invertible matrix S such that the transformations from (A,H) to (S−1AS,SHS) brings the matrix A in Jordan form and simultaneously brings H into a canonical form. Canonical forms for such pairs of matrices already exist in the literature, the goal of the present paper is to add one more canonical form which specifically keeps A in Jordan form, in contrast to the existing canonical forms.

Original languageEnglish
Pages (from-to)282-298
Number of pages17
JournalLinear Algebra and its Applications
Volume623
Early online date15 Apr 2020
DOIs
Publication statusPublished - 15 Aug 2021

Bibliographical note

Publisher Copyright:
© 2020 The Author(s)

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

  • Canonical forms
  • H-unitary
  • Skew-field of quaternions

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