Optical eigenmodes describe coherent solutions of Maxwells equations that are orthogonal to each other. These modes form a natural basis set of the electromagnetic Hilbert space that can be used to describe optical scattering interactions in a simple way. Many of the properties defined in quantum mechanics can formally be found in the optical eigenmodes framework. For example, the Hilbert spaces defined by two different scattering operators are separable only if the two operators commute with each other. Here, we expand the optical eigenmode framework to partially coherent light fields. In this case, we remark that the eigenmode decomposition of partially coherent fields leads to a formalism similar to the density matrix formalism used in quantum mechanics.