The General Solution of Quaternion Matrix Equation Having η-Skew-Hermicity and Its Cramer’s Rule

The General Solution of Quaternion Matrix Equation Having η-Skew-Hermicity and Its Cramer’s Rule

We determine some necessary and sufficient conditions for the existence of the η-skew-Hermitian solution to the following system AX-(AX)η⁎+BYBη⁎+CZCη⁎=D,Y=-Yη⁎,Z=-Zη⁎ over the quaternion skew field and provide an explicit expression of its general solution. Within the framework of the theory of quat...

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Main Authors: Abdur Rehman, Ivan Kyrchei, Ilyas Ali, Muhammad Akram, Abdul Shakoor
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2019/7939238
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spelling doaj-de35b5e4d9e84a608c5ae3e0219eb82a2020-11-25T01:32:31ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/79392387939238The General Solution of Quaternion Matrix Equation Having η-Skew-Hermicity and Its Cramer’s RuleAbdur Rehman0Ivan Kyrchei1Ilyas Ali2Muhammad Akram3Abdul Shakoor4University of Engineering & Technology, Lahore, PakistanPidstrygach Institute for Applied Problems of Mechanics and Mathematics of NASU, Lviv, UkraineUniversity of Engineering & Technology, Lahore, PakistanUniversity of Engineering & Technology, Lahore, PakistanKhawaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, PakistanWe determine some necessary and sufficient conditions for the existence of the η-skew-Hermitian solution to the following system AX-(AX)η⁎+BYBη⁎+CZCη⁎=D,Y=-Yη⁎,Z=-Zη⁎ over the quaternion skew field and provide an explicit expression of its general solution. Within the framework of the theory of quaternion row-column noncommutative determinants, we derive its explicit determinantal representation formulas that are an analog of Cramer’s rule. A numerical example is also provided to establish the main result.http://dx.doi.org/10.1155/2019/7939238
collection DOAJ
language English
format Article
sources DOAJ
author Abdur Rehman
Ivan Kyrchei
Ilyas Ali
Muhammad Akram
Abdul Shakoor
spellingShingle Abdur Rehman
Ivan Kyrchei
Ilyas Ali
Muhammad Akram
Abdul Shakoor
The General Solution of Quaternion Matrix Equation Having η-Skew-Hermicity and Its Cramer’s Rule
Mathematical Problems in Engineering
author_facet Abdur Rehman
Ivan Kyrchei
Ilyas Ali
Muhammad Akram
Abdul Shakoor
author_sort Abdur Rehman
title The General Solution of Quaternion Matrix Equation Having η-Skew-Hermicity and Its Cramer’s Rule
title_short The General Solution of Quaternion Matrix Equation Having η-Skew-Hermicity and Its Cramer’s Rule
title_full The General Solution of Quaternion Matrix Equation Having η-Skew-Hermicity and Its Cramer’s Rule
title_fullStr The General Solution of Quaternion Matrix Equation Having η-Skew-Hermicity and Its Cramer’s Rule
title_full_unstemmed The General Solution of Quaternion Matrix Equation Having η-Skew-Hermicity and Its Cramer’s Rule
title_sort general solution of quaternion matrix equation having η-skew-hermicity and its cramer’s rule
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2019-01-01
description We determine some necessary and sufficient conditions for the existence of the η-skew-Hermitian solution to the following system AX-(AX)η⁎+BYBη⁎+CZCη⁎=D,Y=-Yη⁎,Z=-Zη⁎ over the quaternion skew field and provide an explicit expression of its general solution. Within the framework of the theory of quaternion row-column noncommutative determinants, we derive its explicit determinantal representation formulas that are an analog of Cramer’s rule. A numerical example is also provided to establish the main result.
url http://dx.doi.org/10.1155/2019/7939238
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