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,S⁎HS) 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 language | English |
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Pages (from-to) | 282-298 |
Number of pages | 17 |
Journal | Linear Algebra and its Applications |
Volume | 623 |
Early online date | 15 Apr 2020 |
DOIs | |
Publication status | Published - 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