Flavor SU(3) Cartan generators ($\mathrm{tr}(h_i{h}_j)={\delta }_{ij}$)

For flavor symmetry acting on $(u,d,s)$, trace-orthonormal Hermitian diagonal generators are $h_1=\mathrm{diag}(1,-1,0)/\sqrt{2}$ and $h_2=\mathrm{diag}(1,1,-2)/\sqrt{6}$. The isospin and flavor hypercharge operators are $I_3=h_1/\sqrt{2}$ and $Y=\sqrt{2/3}{h}_2$. Their multiples by $i$ lie in the compact SU(3) Lie algebra.