Gauge-boson mass matrix from an adjoint scalar ($(M^2{)}_{ab}=-2g^2\mathrm{Tr}([t^a,{\Phi }_0][t^b,{\Phi }_0])$)

For generators normalized by $\mathrm{Tr}(t^a{t}^b)={\delta }^{ab}/2$, a constant adjoint vacuum expectation value ${\Phi }_0$ gives this matrix. A generator commuting with ${\Phi }_0$ corresponds to a massless gauge boson.