Abstract
This paper first studies the solution of a complex matrix equation X – AXB = C, obtains an explicit solution of the equation by means of characteristic polynomial, and then studies the quaternion matrix equation \( X - A\tilde{X}B = C \)characterizes the existence of a solution to the matrix equation, and derives closed–form solutions of the matrix equation in explicit forms by means of real representations of quaternion matrices. This paper also gives an application to the complex matrix equation \( X - A\bar{X}B = C. \)
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Supported by the National Natural Science Foundation of China (10371044) and Shanghai Priority Academic Discipline Foundation, Shanghai, China
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Jiang, T.S., Wei, M.S. On a Solution of the Quaternion Matrix Equation \( X - A\tilde{X}B = C \)and Its Application. Acta Math Sinica 21, 483–490 (2005). https://doi.org/10.1007/s10114-004-0428-x
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DOI: https://doi.org/10.1007/s10114-004-0428-x