Two reduced octet matrix elements ($⟨B_r|V_i|B_s⟩=D{d}_{ris}+iF{f}_{ris}$)

An octet operator between baryon octet states has two reduced matrix elements, because the tensor square of the SU(3) adjoint representation contains two octets. The symmetric invariant $d_{ris}$ and antisymmetric invariant $f_{ris}$ give independent component tensors. Equivalently, represent baryons by traceless matrices $B$ and let the operator act as $F[t_i,B]+D(\{t_i,B\}-\frac{2}{3}\mathrm{tr}(t_{i}B)I)$. Normalization choices are absorbed into $F,D$; Hermitian operators permit real coefficients in a Hermitian octet basis.