An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications

An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications

This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices. It sets up an algebraic bridge between consimilarity and similarity, and turns the theory of...

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Main Authors: Tongsong Jiang, Xuehan Cheng, Sitao Ling
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/795203
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spelling doaj-2722f64c13b842868e28f0e4cc31f7c22020-11-24T23:47:37ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/795203795203An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and ApplicationsTongsong Jiang0Xuehan Cheng1Sitao Ling2College of Science, Linyi University, Linyi, Shandong 276005, ChinaCollege of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, ChinaState Key Laboratory for Geomechanics and Deep Underground Engineering, Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, ChinaThis paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices. It sets up an algebraic bridge between consimilarity and similarity, and turns the theory of consimilarity of quaternion matrices into that of ordinary similarity of complex matrices. This paper also gives algebraic methods for finding coneigenvalues and coneigenvectors of quaternion matrices by means of complex representation of a quaternion matrix.http://dx.doi.org/10.1155/2014/795203
collection DOAJ
language English
format Article
sources DOAJ
author Tongsong Jiang
Xuehan Cheng
Sitao Ling
spellingShingle Tongsong Jiang
Xuehan Cheng
Sitao Ling
An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
Journal of Applied Mathematics
author_facet Tongsong Jiang
Xuehan Cheng
Sitao Ling
author_sort Tongsong Jiang
title An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
title_short An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
title_full An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
title_fullStr An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
title_full_unstemmed An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
title_sort algebraic relation between consimilarity and similarity of quaternion matrices and applications
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices. It sets up an algebraic bridge between consimilarity and similarity, and turns the theory of consimilarity of quaternion matrices into that of ordinary similarity of complex matrices. This paper also gives algebraic methods for finding coneigenvalues and coneigenvectors of quaternion matrices by means of complex representation of a quaternion matrix.
url http://dx.doi.org/10.1155/2014/795203
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AT xuehancheng analgebraicrelationbetweenconsimilarityandsimilarityofquaternionmatricesandapplications
AT sitaoling analgebraicrelationbetweenconsimilarityandsimilarityofquaternionmatricesandapplications
AT tongsongjiang algebraicrelationbetweenconsimilarityandsimilarityofquaternionmatricesandapplications
AT xuehancheng algebraicrelationbetweenconsimilarityandsimilarityofquaternionmatricesandapplications
AT sitaoling algebraicrelationbetweenconsimilarityandsimilarityofquaternionmatricesandapplications
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