 Gram-Schmidt yields an inferior solution, shown by a Frobenius distance of 8.28659 instead of the minimum 8.12404.Some numerical applications, such as Monte Carlo methods and exploration of high-dimensional data spaces, require generation of uniformly distributed random orthogonal matrices.In this context, "uniform" is defined in terms of Haar measure, which essentially requires that the distribution not change if multiplied by any freely chosen orthogonal matrix.