Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 795203, 5 pages
Research Article

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

1College of Science, Linyi University, Linyi, Shandong 276005, China
2College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China
3College of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, China
4State Key Laboratory for Geomechanics and Deep Underground Engineering, Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

Received 12 May 2014; Revised 15 August 2014; Accepted 21 August 2014; Published 1 September 2014

Academic Editor: Fan Min

Copyright © 2014 Tongsong Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.