I think the GP is trying to make the point that, a scalar in most numerical physics contexts is either a real or complex double precision floating point number(like a double), but they don't see how someone would represent a vector in this geometric algebra(a matrix in Eigen? or a vector in Eigen? myself I would just use a vector, but the GP was interested in the oriented part and seeemed confused). I believe they were looking for an example of someone using this in practice to solve a real problem and have some explanation of the choices made.