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

Author

Listed:
  • Abdur Rehman
  • Ivan Kyrchei
  • Muhammad Akram
  • Ilyas Ali
  • Abdul Shakoor

Abstract

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.

Suggested Citation

  • Abdur Rehman & Ivan Kyrchei & Muhammad Akram & Ilyas Ali & Abdul Shakoor, 2019. "Least‐Norm of the General Solution to Some System of Quaternion Matrix Equations and Its Determinantal Representations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnlaaa:v:2019:y:2019:i:1:n:9072690
    DOI: 10.1155/2019/9072690
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    References listed on IDEAS

    as
    1. Ivan I. Kyrchei, 2018. "Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations," Journal of Mathematics, Hindawi, vol. 2018, pages 1-12, November.
    2. Song, Guang-Jing & Wang, Qing-Wen & Yu, Shao-Wen, 2018. "Cramer’s rule for a system of quaternion matrix equations with applications," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 490-499.
    3. Rehman, Abdur & Wang, Qing-Wen & He, Zhuo-Heng, 2015. "Solution to a system of real quaternion matrix equations encompassing η-Hermicity," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 945-957.
    4. Kyrchei, Ivan, 2015. "Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 453-465.
    5. Rehman, Abdur & Wang, Qing-Wen, 2015. "A system of matrix equations with five variables," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 805-819.
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