On a Solution of the Quaternion Matrix Equation {A \tilde{X} -X B = C} and Its Applications |
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Authors: | Tongsong Jiang Sitao Ling |
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Institution: | 1. Department of Mathematics, Linyi University, Shandong, China 2. Department of Computer Science and Technology, Shandong University, Shandong, China 3. Department of Mathematics, China University of Mining and Technology, Jiangsu, China
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Abstract: | This paper studies the problem of solution of the quaternion matrix equation ${A \tilde{X} -X B = C}$ by means of real representation of a quaternion matrix, derives a similarity version of Roth’s theorem for the existence of solution to the quaternion matrix equation, and obtains closed-form solutions of the quaternion matrix equation in explicit forms. As a special case, this paper also gives some applications of the solutions of complex matrix equation ${A \bar{X} -X B = C}$ and of the consimilarity of complex matrices. |
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