Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations
Joint Authors
Kyrchei, Ivan
Rehman, Abdur
Akram, Muhammad
Ali, Ilyas
Shakoor, Abdul
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-08-19
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We constitute some necessary and sufficient conditions for the system A1X1=C1, X1B1=C2, A2X2=C3, X2B2=C4, A3X1B3+A4X2B4=Cc, to have a solution over the quaternion skew field in this paper.
A novel expression of general solution to this system is also established when it has a solution.
The least norm of the solution to this system is also researched in this article.
Some former consequences can be regarded as particular cases of this article.
Finally, we give determinantal representations (analogs of Cramer’s rule) of the least norm solution to the system using row-column noncommutative determinants.
An algorithm and numerical examples are given to elaborate our results.
American Psychological Association (APA)
Rehman, Abdur& Kyrchei, Ivan& Akram, Muhammad& Ali, Ilyas& Shakoor, Abdul. 2019. Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations. Abstract and Applied Analysis،Vol. 2019, no. 2019, pp.1-18.
https://search.emarefa.net/detail/BIM-1114508
Modern Language Association (MLA)
Rehman, Abdur…[et al.]. Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations. Abstract and Applied Analysis No. 2019 (2019), pp.1-18.
https://search.emarefa.net/detail/BIM-1114508
American Medical Association (AMA)
Rehman, Abdur& Kyrchei, Ivan& Akram, Muhammad& Ali, Ilyas& Shakoor, Abdul. Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations. Abstract and Applied Analysis. 2019. Vol. 2019, no. 2019, pp.1-18.
https://search.emarefa.net/detail/BIM-1114508
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1114508
