  The shell model solve the nuclear many-body problem in a restricted model
space and takes into account the restricted nature of the space by using
effective interactions and operators. In this paper two different methods for
generating the effective interactions are considered. One is based on a partial
solution of the Schrodinger equation (Bloch-Horowitz or the Feshbach projection
formalism) and other on linear algebra (Lee-Suzuki). The two methods are
derived in a parallel manner so that the difference and similarities become
apparent. The connections with the renormalization group are also pointed out.
