I read that one can find a single normal equation in n dimensions by taking n-1 vectors, for example:
in 2d one can find just 2 equations that are perpendicular to a single line (the two being anti-parallel and coincident to each other). While in 3d a single line has an infinite number of orthogonal solutions, to narrow these down to 2 solutions (same as before, them being anti-parallel and coincident to each other, a second vector is needed and a cross product is done.
A cross product will not work in 4d, so how could I get a solution for a normal line with 3 vectors in 4d? I know how to test if a given vector is perpendicular to the others in 4d, but I don't know a way to find such a vector other than trial and error.
Best Answer
Have you tried
http://en.wikipedia.org/wiki/Cross_product#Generalizations
the multilinear algebra section?