i need to sample the N-dimensional subspaces of a M-dimensional linear space over C uniformly. That is, all subspaces are sampled with equal probability how should i do it? would this work? First generate a M*N matrix, the real and imaginary parts of each element is sampled from the normal distribution. Then by using QR decomposition, i can get N orthonormal vectors, which span a N-dimensional subspace. Take it.