Resumen de On matrix equations X-AXF=C and X-AX_F=C

Ai-Guo Wu, Hao-Qian Wang, Guang-Ren Duan

• With the help of the concept of Kronecker map, an explicit solution for the matrix equation X-AXF=C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation is also studied. An explicit solution for this matrix equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices.