[…] A permutation matrix is an invertible matrix that changes the orders of columns or rows. The inverse of a permutation matrix equals its transpose. Thus, for any two-factor decomposition Y = L*R, you can permute the columns of L and simultaneously permute the rows of R by using a permutation matrix, P, as follows: Y = (L*P) (P`*R). This is known as the order ambiguity or the permutation ambiguity. For example, the following IML program interchanges the order of the columns of L and the rows of R, and the product is the same: …