Maxwell Wave Equation (continued)

The above linear algebra two-step analysis of an overdetermined (but consistent) system $A\vec u = \vec b$ is an invaluable guide in solving Maxwell's wave equation

$$\mathcal A \left[ \begin{array}{c} \phi\\ A_z\\ A_x\\ A_y \end{ar... ...array}{c} ~\\ ~ \end{array}\right\} \textrm{transverse components}, \end{array}$$ (661)