Since the flavour rotations A are approximate, not exact, symmetries, each orthogonal state in the vector space corresponds to a different particle species. In the example above, when a proton is transformed by every possible flavour rotation A, it turns out that it moves around an 8 dimensional vector space. Those 8 dimensions correspond to the 8 particles in the so-called "baryon octet" (proton, neutron, Σ, Σ, Σ, Ξ, Ξ, Λ). This corresponds to an 8-dimensional ("octet") representation of the group SU(3). Since A is an approximate symmetry, all the particles in this octet have similar mass.