I. Geometric Matrix Recovery
Without loss of generality, we assume that has pairwise linearly independent columns, and . BMMR tries to identify in given , where is assumed to be statistically independent. Obviously, this can only be done up to equivalence [3], where is said to be equivalent to , , if can be written as with an invertible diagonal matrix (scaling matrix) and an invertible matrix with unit vectors in each row (permutation matrix). Hence, we may assume the columns of to have unit norm.