The General Solution to a Classical Matrix Equation <i>AXB</i> = <i>C</i> over the Dual Split Quaternion Algebra

oleh: Kai-Wen Si, Qing-Wen Wang

Format: Article
Diterbitkan: MDPI AG 2024-04-01

Deskripsi

In this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>X</mi><mi>B</mi><mo> </mo><mo>=</mo><mo> </mo><mi>C</mi></mrow></semantics></math></inline-formula>, and present the general solution expression when the solvability conditions are met. As an application, we delve into the necessary and sufficient conditions for the existence of a Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>X</mi><mo> </mo><mo>=</mo><mo> </mo><mi>C</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>X</mi><mi>B</mi><mo> </mo><mo>=</mo><mo> </mo><mi>C</mi></mrow></semantics></math></inline-formula>. Finally, we provide a numerical example to demonstrate the findings of this paper.