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

```

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