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

Author

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

Abstract

We determine some necessary and sufficient conditions for the existence of the - skew-Hermitian solution to the following system 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.

Suggested Citation

  • Abdur Rehman & Ivan Kyrchei & Ilyas Ali & Muhammad Akram & Abdul Shakoor, 2019. "The General Solution of Quaternion Matrix Equation Having - Skew-Hermicity and Its Cramer’s Rule," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-25, July.
    • Handle: RePEc:hin:jnlmpe:7939238
    DOI: 10.1155/2019/7939238
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