Hermite Positive Definite Solution of the Quaternion Matrix Equation <i>X<sup>m</sup> + B*XB = C</i>
Yiwen Yao,
Guangmei Liu,
Yanting Zhang
et al.
Abstract:This paper discusses the necessary and sufficient conditions for the existence of Hermite positive definite solutions of the quaternion matrix equation X m + B * XB = C (m > 0) and its iterative solution method. According to the characteristics of the coefficient matrix, a corresponding algebraic equation system is ingeniously constructed, and by discussing the equation system's solvability, the matrix equation's existence interval is obtained. Based on the characteristics of the coefficient matrix, some neces… Show more
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