Is it possible to generate a N*D random matrix with columns of unit length?
If not, I also think it is possible of generating a N*D random matrix and, after that, normalizing it in order to have columns of unit length.
Is this last case, how is this possible mathematically?
If you want the column vectors to be uniformly distributed on the unit sphere, you may first generate an $N\times D$ rectangular array of standard normal pseudorandom numbers, and then normalise the length of each column vector.