If "n" > 4, then there is an orthogonal decomposition into (unique) irreducible subspaceswhere:formula_26, where formula_27 is the space of real scalars:formula_28, where "S""V" is the space of trace-free symmetric 2-forms:formula_29The parts "S", "E", and "C" of the Ricci decomposition of a given Riemann tensor "R" are the orthogonal projections of "R" onto these invariant factors.
If "n" ≥ 4, then there is an orthogonal decomposition into (unique) irreducible subspaceswhere: formula_26: formula_27, where "S""V" is the space of trace-free symmetric 2-forms: formula_28The parts "S", "E", and "C" of the Ricci decomposition of a given Riemann tensor "R" are the orthogonal projections of "R" onto these invariant factors.