Gradient matrices are formulated for the linear multivariable system with output feedback. The incremental motion of the poles and zeros and the coefficients of the numerator and denominator transfer function polynomials is determined as a function of the elements of an output feedback gain matrix. Also considered is the incremental movement of zeros and the coefficients of the numerator transfer function polynomials with respect to the elements of an input gain matrix. In addition, the characteristic polynomial gradient results are used to study the bounds on the number of independently assignable poles for linear multivariable systems with constant output feedback. The investigation is extended to estimate the minimum order dynamic output feedback compensator necessary to establish full polo placement for the expanded order system. Examples are included to illustrate the methods involved and to make comparisons with previous results.