<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, we give some equivalence relations and results over the commutative quaternions and their matrices. In this sense, consimilarity, semisimilarity, and consemisimilarity over the commutative quaternion algebra and commutative quaternion matrix algebra are established. Equalities of these equivalence relations are explicitly determined. Also Syvester-s-Conjugate commutative quaternion matrix equations are studied by means of real representation of the commutative quaternion matrices and consimilarity of the two commutative quaternion matrices.</p></abstract>

In this paper, we give some equivalence relations and results over the commutative quaternions and their matrices. In this sense, consimilarity, semisimilarity, and consemisimilarity over the commutative quaternion algebra and commutative quaternion matrix algebra are established. Equalities of these equivalence relations are explicitly determined. Also Syvester-s-Conjugate commutative quaternion matrix equations are studied by means of real representation of the commutative quaternion matrices and consimilarity of the two commutative quaternion matrices.

Some Equivalence Relations and Results over the Commutative Quaternions and Their Matrices

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

In this paper, we give some equivalence relations and results over the commutative quaternions and their matrices. In this sense, consimilarity,...

Some Equivalence Relations and Results over the Commutative Quaternions and Their Matrices

Published Online: Mar 31, 2018

Page range: 125 - 142

Received: Nov 20, 2016

Accepted: Dec 21, 2016

DOI: https://doi.org/10.1515/auom-2017-0040

Keywords
Commutative quaternion, equivalence relation, coneigenvalue, Slyvester conjugate matrix equation

© 2018

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

Some Equivalence Relations and Results over the Commutative Quaternions and Their Matrices

Published Online: Mar 31, 2018

Page range: 125 - 142

Received: Nov 20, 2016

Accepted: Dec 21, 2016

DOI: https://doi.org/10.1515/auom-2017-0040

KeywordsCommutative quaternion, equivalence relation, coneigenvalue, Slyvester conjugate matrix equation

© 2018

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

Keywords
Commutative quaternion, equivalence relation, coneigenvalue, Slyvester conjugate matrix equation