A representation of the general common solution to the matrix equations A(1)XB(1)=C-1 and A(2)XB(2)=C-2 with applications
We give new necessary and sufficient conditions for the existence of a common solution to the pair of linear matrix equations A(1)XB(1) = C-1 and A(2)XB(2) = C-2 and derive a new representation of the general common solution to these two equations. We apply this result to determine new necessary and sufficient conditions for the existence of an Hermitian solution and a representation of the general Hermitian solution to the matrix equation AXE = C. (C) 2001 Elsevier Science Ltd. All rights reserved.
simultaneous matrix equations vec operator invec operator kronecker matrix product conditional inverse