On a particular case of the inconsistent linear matrix equation AX+YB=C

AbstractWe consider the linear matrix equation AX+YB=C where A,B, and C are given matrices of dimensions (r+1)×r, s×(s+1), and (r+1)×(s+1), respectively, and rank A = r, rank B = s. We give a connection between the least-squares solution and the solution which minimizes an arbitrary norm of the residual matrix C−AX− YB