 Orthogonalizing matrices with independent uniformly distributed random entries does not result in uniformly distributed orthogonal matrices, but the decomposition of independent normally distributed random entries does, as long as the diagonal of contains only positive entries .replaced this with a more efficient idea that later generalized as the "subgroup algorithm" (in which form it works just as well for permutations and rotations).To generate an orthogonal matrix, take an one and a uniformly distributed unit vector of dimension .