Compact forms of reduced density matrices

The objective of this paper is to identify the necessary and sufficient minimum information carried by Reduced Density Matrices (RDMs). This minimum of essential information determines a set of equivalent compact-form matrices that are devoid of the redundant information present in the original RDMs when the system possesses symmetry invariances. The basic properties and algebra operations of these compact-form matrices are obtained here. The use of these new mathematical objects renders far more economical the operations and storage of RDMs and will thus be of interest in the study of systems with symmetry invariances. In particular, it opens the possibility of using large basis for medium-sized systems when solving iteratively the contracted Schrödinger equation.