Fermion mass matrix
= Fermion mass matrix
{title2=$-\bar f_LM_ff_R+\mathrm{h.c.}$}
After a scalar vacuum expectation value, a <Yukawa matrix> produces a bilinear $-\bar f_LM_ff_R+\mathrm{h.c.}$. Independent unitary left/right rotations diagonalize $M_f$ with nonnegative masses. Extra scalar-dependent operators can make the physical scalar coupling matrix fail to diagonalize with the mass matrix.