ON SOLUTIONS OF MATRIX EQUATION AXB+CYD = F

In this paper, the matrix equation with two unknown matrices X, Y of f orm AXB + CYD = F is discussed. By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain expressions of the leas t-squares solutions of the matrix equation, and sufficient and necessa ry conditions for the existence and uniqueness of the solutions. We al so derive a general form of the solutions. We also study the least-squ ares Hermitian (skew-Hermitian) solutions of equation AXA(H)+CYCH=F. ( C) 1998 Elsevier Science Inc. All rights reserved.