APPLICATIONS OF LINEAR TRANSFORMATIONS TO MATRIX EQUATIONS

We consider the linear transformation T(X) = AX - CXB where A, C is an element of M-n, B is an element of M-s. We Show a new approach to obt aining conditions for the existence and uniqueness of the solution X o f the matrix equation T(X) = R. As a consequence of our approach we pr esent a simple characterization of a full-rank solution to the matrix equation. We apply the existence theorem to a general form of the obse rver matrix equation and characterize the existence of a full-rank sol ution. (C) 1997 Elsevier Science Inc.