  Quantization of the noncommutative geometric spectral action has so far been
performed on the final component form of the action where all traces over the
Dirac matrices and symmetry algebra are carried out. In this work, in order to
preserve the noncommutative geometric structure of the formalism, we derive the
quantization rules for propagators and vertices in matrix form. We show that
the results in the case of a product of a four-dimensional Euclidean manifold
by a finite space, could be cast in the form of that of a Yang-Mills theory. We
illustrate the procedure for the toy electroweak model.
