Least-Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations

Autor: Abdur Rehman, Ivan Kyrchei, Muhammad Akram, Ilyas Ali, Abdul Shakoor
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Abstract and Applied Analysis, Vol 2019 (2019)
Druh dokumentu: article
ISSN: 1085-3375
1687-0409
DOI: 10.1155/2019/9072690
Popis: 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.
Databáze: Directory of Open Access Journals
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