Like the case for regular spin, the isospin operator I is vector -valued: it has three components I x, I y, I z, which are coordinates in the same 3-dimensional vector space where the 3 representation acts. Note that this vector space has nothing to do with the physical space, except similar mathematical formalism. Isospin is described by two quantum numbers : I – the total isospin, and I 3 – an eigenvalue of the I z projection for which flavor states are eigenstates. In other words, each I 3 state specifies certain flavor state of a multiplet. The third coordinate (z), to which the "3" subscript refers, is chosen due to notational conventions that relate bases in 2 and 3 representation spaces. Namely, for the spin- ⁠ 1 / 2 ⁠ case, components of I are equal to Pauli matrices divided by 2, and so I z = ⁠ 1 / 2 ⁠ τ 3, where