We derive exact relationships for the reduced density matrices in representations where the transformation matrix is a product of one‐body transformation matrices. We specialize to the momentum and onebody energy representations. By decoupling the equations we are able to write the Hartree‐Fock equation in terms of the first‐order density matrix in an arbitrary representation. Applications to reduced local energy and the correlation problem are discussed. Copyright © 1986 John Wiley & Sons, Inc.