This paper investigates the problem of determining a general family of output feedback matricesKwhich drive the eigenvalues of a controllable and observable linear time-invariant system to desired prespecified positions. The approach followed is based on the concept of making the closed-loop system matrixA+BKCsimilar to another matrixHof the same dimensions which possesses the desired closed-loop eigenvalues. This approach reduces the problem of determining a general family ofK's to that of solving a linear set of equations. In addition, necessary conditions are established for stabilizing and arbitrarily assigning all eigenvalues by output feedback.