Non-square case for LU is in fact easy. Note that if you have A=LU as a block matrix A11 A12 A21 A22
then its LU-factors L and U are L11 0 and U11 U12 L21 L22 0 U22 and A11=L11 U11, A12=L11 U12, A21=L21 U11, A22=L21 U12+L22 U22 Assume that A11 is square and full rank (else one may apply permutations of rows and columns in the usual way). while A21=0 and A22=0. Then one can take L21=0, L22=U22=0, while A12=L11 U12 implies U12=L11^-1 A12. That is, we can first compute LU-decomposition of a square matrix A11, and then compute U12 from it and A. Similarly, if instead A12=0 and A22=0, then we can take U12=0, L22=U22=0, and A21=L21 U11, i.e. L21=A21 U11^-1, and again we compute LU-decomposition of A11, and then L21=A21 U11^-1. ---------------- Note that in some cases one cannot get LU, but instead must go for an PLU,with P a permutation matrix. For non-square matrices this seems a bit more complicated, but, well, still doable. HTH Dima On Mon, Feb 5, 2024 at 6:00 PM Nils Bruin <nbr...@sfu.ca> wrote: > > On Monday 5 February 2024 at 02:31:04 UTC-8 Dima Pasechnik wrote: > > > it is the matter of adding extra zero rows or columns to the matrix you want > to decompose. This could be a quick fix. > > (in reference to computing LU decompositions of non-square matrices) -- in a > numerical setting, adding extra zero rows/columns may not be such an > attractive option: if previously you know you had a maximal rank matrix, you > have now ruined it by the padding. It's worth checking the documentation and > literature if padding is appropriate/desirable for the target > algorithm/implementation. > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/622a01e0-9197-40c5-beda-92729c4e4a32n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq2G0A1Hwvf2iBbrUC42LaNVrVm_OTiLSJpCkjhjJvEpWQ%40mail.gmail.com.
