Two new simple, complete. analytical. and restrietion-free soiUtions with complete and explicit freetion of the matrix equation AV+BW=VF are proposed. Here IA BJ is know and is control-lable, and F is in the Jordan form with arbitrary given eigenvalues-Based on the proposed solutions of this matrix equation. a complete parametric approach for eigenstructure assignment in liner. systems via state feedback is proposed, and two new algorithms are presented. The Proposed solutions of the lilatrix equation and the eigenstructure assign-merit result are generalizations of some previous results and are simpler and more effectice.