The Generalized Electromagnetic Projection Operator Over a 3 Dimension Probabilistic Space

In a recent paper we discovered the existence of a hidden symmetry in a two-dimensional probabilistic space associated to projection operators, also we showed that projection operators help us to give a particular representation of the solutions of the Fredholm integral equations that merge for a broadcasting situation. Now, we explore the case for a three-dimension probabilistic space applied to the representation of the electromagnetic resonant vector (ERV) and for the generalized source (GS) and ask about the possible recover of symmetry properties if we scaled to a higher dimension and, as we have said, give it a useful application. Because for three dimensions there is a simple representation for the symmetry group associated with these operators, so in this work we explicitly construct a matrix representation, which makes us think that it is possible to find hidden symmetries for higher dimensions. For the two-dimensional case, we find a space that contains the originally constructed probabilistic space, but it shows that the concept of probability is immanent to the existence of a space we call the dual space, like in the jargon of quantum mechanics. First, we remember the orthogonality properties of the ERV