Hi! On 2012-07-02, Martin Albrecht <martinralbre...@googlemail.com> wrote: > Shouldn't both give the same distribution mod p? Since every non-singular > matrix A has a LU decomposition we should be able to just sample L and U > separately to produce A?
Sorry for my ignorance, but is it really the case that an LU decomposition exists for all invertible matrices? I thought there may only be an LUP decomposition. If I am not mistaken, the LU decomposition is unique if one requires that L (or U) has only 1 on the diagonal. Because of the uniqueness, I'd expect that putting 1 on the diagonal of L and choosing the entries of U and the remaining of L randomly equally distributed yields a reasonable distribution of invertible matrices. However, if it is really the case that we must consider LUP decompositions, then I am not totally convinced that a nicely distributed random choice of a permutation matrix P on top of the choice of L and U as above yields a nice distribution of invertible matrices. Cheers, Simon -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
