标题：On a Solution of the Quaternion Matrix Equation and Its Applications
作者：Jiang, Tongsong; Ling, Sitao
作者机构：[Jiang, Tongsong] Linyi Univ, Dept Math, Linyi, Shandong, Peoples R China.; [Jiang, Tongsong] Shandong Univ, Dept Comp Sci & Technol, Jinan, Shandon 更多
通讯作者地址：[Jiang, TS]Linyi Univ, Dept Math, Linyi, Shandong, Peoples R China.
来源：ADVANCES IN APPLIED CLIFFORD ALGEBRAS
关键词：Consimilarity; quaternion; real representation
摘要：This paper studies the problem of solution of the quaternion matrix equation 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 and of the consimilarity of complex matrices.