the only way to ensure that the matrices
a real matrix,
is by selecting a proper choice of complex initial conditions for both matrices.
As shown by the literature such proper choice is a matter of intense debate,
seemingly not yet solved.
There are however particular choices of real
which are relevant for the discussion of Gaussian beams.
Due to such relevance those choices are presented in this section for the case of a point source
and for the case of a linear source.
Orlando Camargo Rodríguez