<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability conditions and general solutions of the equations <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2016-0054_001.jpg"></inline-graphic> and <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2016-0054_002.jpg"></inline-graphic> in split quaternions and split quaternion matrices, respectively. Moreover, coneigenvalue and coneigenvector are defined for split quaternion matrices. Some consequences are also presented. </p></abstract>

In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability conditions and general solutions of the equations  and  in split quaternions and split quaternion matrices, respectively. Moreover, coneigenvalue and coneigenvector are defined for split quaternion matrices. Some consequences are also presented.

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"On the Consimilarity of Split Quaternions and Split Quaternion Matrices"}

In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability...

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Published Online: Sep 21, 2017

Page range: 189 - 207

Received: Dec 07, 2015

Accepted: Feb 16, 2016

DOI: https://doi.org/10.1515/auom-2016-0054

Keywords
Split quaternion, Split quaternion matrix, Consimilarity, Coneigenvalue

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Published Online: Sep 21, 2017

Page range: 189 - 207

Received: Dec 07, 2015

Accepted: Feb 16, 2016

DOI: https://doi.org/10.1515/auom-2016-0054

KeywordsSplit quaternion, Split quaternion matrix, Consimilarity, Coneigenvalue

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Split quaternion, Split quaternion matrix, Consimilarity, Coneigenvalue