Geometry of density matrices. III. Spin components

A definition is given for the spin‐tensorial components of a p‐electron density matrix for arbitrary p. Certain of these are defined to be standard components, and it is shown that all others can be obtained from them by linear combinations of permutations. When the density matrix is reduced, the standard components either map into standard components of the fewer‐electron density matrix or into the origin. One‐ and two‐electron density matrices are treated in greater detail. Reducing bases are given for the spaces in which the spatial coefficients of the spin components are elements. For spin eigenstates traces of all components are determined, and the π = 1 parts of all components are determined in terms of two independent components, which are themselves determined by the two‐electron charge density matrix. Geometric consequences are investigated.