Special decomposition of a rectangular matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg71573] Special decomposition of a rectangular matrix*From*: Marco Gabiccini <m.gabiccini at ing.unipi.it>*Date*: Thu, 23 Nov 2006 05:41:45 -0500 (EST)

Dear Group, I have an m x n matrix A with rank(A) = r. (with m > n) I look at matrix A as a block matrix A = {{A1},{A2}} with A1 p by n and A2 (m-p) by n, that is: A = [ A1 ] [ A2 ]; How can I find if it is possible to decompose matrix A in the following form A = [ O B12 B13] [ B21 B22 O ] and if yes, which algorithm (or combination of algorithms) performs this? By the way, does anyone know if an algorithm for performing LU Decomposition for rectangular matrices exists already in Mathematica? Thanks, Marco Gabiccini Ing. Marco Gabiccini, PhD Dept. of Mechanical, Nuclear and Production Engineering University of Pisa Via Diotisalvi, 2, 56126 Pisa (PI) - Italy Phone: +39-050-836.676 E-mail: m.gabiccini at ing.unipi.it