On the solution to the Sylvester matrix equation AV+BW=EVF

A simple, direct, complete and explicit parametric solution of the generalized Sylvester matrix equation AV+BW=EVF is proposed for matrix F in the Jordan form with arbitrary eigenvalues using the Smith canonical form of the matrix [A-sE B]. The obtained solution is in a clear, neat form and may have important applications in descriptor linear system theory.