The diagonal and off-diagonal vibrational interactions in the amide I subspace are examined for the oligomers and hydration clusters of N-methylacetamide (NMA). A method called the average partial vector method is developed for constructing the force constant matrix (F matrix) in the amide I subspace from that in the full Cartesian space. It is shown that the F matrix thus constructed can reproduce quantitatively the vibrational frequencies and vibrational patterns of the amide I modes calculated in the full Cartesian space. For the NMA oligomers consisting of three or more NMA molecules, the cooperative effect on the C=O bond length (and on the diagonal force constant of the amide I mode as well) is seen. Including the values for those oligomers, the shifts in the diagonal terms in the amide I subspace (deltak(1)) and in the C=O bond length (deltaSc=o) of the NMA oligomers and NMA-water clusters from the values of an isolated NMA molecule are approximately proportional to each other. In addition, deltaSc=o is shown to be approximately proportional to the electric field (originating from the other molecules in the NMA oligomer or NMA-water cluster) evaluated at a specified point on the C=O bond, indicating that the origin of the cooperative effect is the enhancement of the electric field operating among the molecules. The effect of mechanical anharmonicity on deltak(1), is examined by introducing the internal-normal mixed coordinate system representation for the cubic force constants, and is shown to overestimate the variation of deltak(1),. The partial cancellation by the effect of electrical anharmonicity (dipole second derivative) is also important. For the off-diagonal terms, it is shown that the TDC model provides a good approximation. However, for the (small) coupling constants between distant peptide groups, the effect of the polarization of the intervening peptide group(s) (also called the third-body mediation and may be regarded as a dipole-induced dipole effect) is also recognized.