Pairs of Hermitian and skew-Hermitian quaternionic matrices: canonical forms and their applications
type: Item
instance of: scholarly article
title: Pairs of Hermitian and skew-Hermitian quaternionic matrices: canonical forms and their applications
zbMATH Open document ID: 1149.15013
author: Leiba Rodman
published in: Linear Algebra and its Applications
publication date: 2008-08-06T00:00:00Z
review text: The author describes canonical forms and their applications for pairs of Hermitian and/or skew-Hermitian quaternionic matrices. The paper is mainly expository, and most of the results here are not new, although some applications, corollaries, and auxiliary results perhaps have not been previously observed. Canonical forms are described for pairs of quaternionic matrices, or equivalently matrix pencils, where each one of the matrices is either Hermitian or skew-Hermitian, under strict equivalence and simultaneous congruence. Several applications are developed, including structure of selfadjoint and skew-selfadjoint matrices with respect to a regular sesquilinear quaternion valued form, or with respect to a regular skew-sesquilinear form. Another application gives canonical forms for quaternionic matrices under congruence.
reviewed by: Piwen Yang
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 5307045
zbMATH Keywords: Hermitian matrices
zbMATH Keywords: skew-Hermitian matrices
zbMATH Keywords: quaternionic matrices
zbMATH Keywords: canonical forms
zbMATH Keywords: strict equivalence
zbMATH Keywords: matrix pencils
zbMATH Keywords: simultaneous congruence
zbMATH Keywords: skew-selfadjoint matrices
zbMATH Keywords: skew-sesquilinear form
MaRDI profile type: Publication
full work available at URL: j.laa.2006.12.017
OpenAlex ID: W2055704671
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DOI: 10.1016/J.LAA.2006.12.017
description: scientific article; zbMATH DE number 5307045