We generalized Bloch's formalism to a non-Hermitian Hamiltonian ( H) and presented the application of the resulting theory to the EOM-CC wave functions. We compared Bloch's and Cloizeax's versions of the effective Hamiltonian approach and demonstrated that they perform similarly. The constructed Bloch's and des Cloizeaux's effective Hamiltonians provide a direct way to interpret the EOM-CC wave functions in terms of effective theories.