Abstract
Within the framework of the theory of quaternion column-row determinants and using determinantal representations of the Moore–Penrose inverse previously obtained by the author, we get explicit determinantal representation formulas of solutions (analogs of Cramer’s Rule) to the quaternion two-sided generalized Sylvester matrix equation \( \mathbf{A}_{1}{} \mathbf{X}_{1}{} \mathbf{B}_{1}+ \mathbf{A}_{2}{} \mathbf{X}_{2}{} \mathbf{B}_{2}=\mathbf{C}\) and its all special cases when its first term or both terms are one-sided. Finally, determinantal representations of solutions to like-Lyapunov equations are derived.
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Communicated by G. Stacey Staples
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Kyrchei, I. Cramer’s Rules for Sylvester Quaternion Matrix Equation and Its Special Cases. Adv. Appl. Clifford Algebras 28, 90 (2018). https://doi.org/10.1007/s00006-018-0909-0
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DOI: https://doi.org/10.1007/s00006-018-0909-0
Keywords
- Matrix equation
- Sylvester matrix equation
- Lyapunov matrix equation
- Cramer Rule
- Quaternion matrix
- Noncommutative determinant