Given a linear controllable system Ex = Fx + Gu, we study the limits of linear proportional feedback u = Kx + v in assigning a desired finite and infinite eigenstructure of the closed-loop system Ex = (F + GK)x + Gv. The closed-loop system is not restricted to be regular; its rank makes part of the specifications. Necessary and sufficient conditions are established for the existence of a feedback gain K which assigns the desired eigenstructure, and a procedure is outlined to calculate one such gain.