Use whatever random number generator you like to get values for , , ..., between -1 and 1, then calculate .
I need an algorithm to generate random vectors. Restriction on vectors are as follows:
a) so they lie in an dimensional hyperplane going through zero.
c) The density is uniform, e.g. each vector satisfying conditions a) and b) is picked with equal probability.
Example: and are both OK as long as they are generated with the same probability.