On solutions of matrix equation XF - AX = C and XF-AX? = C over quaternion field

摘要

By means of Kronecker map and complex representation of a quaternion matrix, some explicit solutions to the quaternion matrix equations XF-AX=C and XF-AX=C are established. One of the solutions is neatly expressed by a symmetric matrix, a controllability matrix and an observability matrix. In addition, two practical algorithms for these two equations are given.