LU Decompsoition for singular matrices

• To: mathgroup at smc.vnet.net
• Subject: [mg33253] LU Decompsoition for singular matrices
• From: Muhammad Sabieh Anwar <sabieh at khwarzimic.org>
• Date: Tue, 12 Mar 2002 05:08:40 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Good day

The mathematica LUDeecomposition (I think) is based on the Gauss
elimination technique. Such an elimination cannot be done for singular
matrices. (Or can it be done?)

if A is my singular matrix, then

LUDecomposition[A] returns me a warning alongwith the correct
decompsition

In[154]:=
M3={{1,2,3},{1,2,3},{4,5,6}}
In[156]:=
Lud3=LUDecomposition[M3]

LUDecomposition::sing: Matrix {{1,2,3},{1,2,3},{4,5,6}} is singular.

Out[156]=
{{{1,2,3},{4,-3,-6},{1,0,0}},{1,3,2},1}

In[159]:=
Upper[Lud3[[1,All]]]

Out[159]=
{{1,2,3},{0,-3,-6},{0,0,0}}

In[161]:=
Lower[Lud3[[1,All]]].Upper[Lud3[[1,All]]]

Out[161]=
{{1,2,3},{4,5,6},{1,2,3}}

Any help will be appreciated?
Regards

Sabieh Anwar
Centre for Qunatum Computation
University of Oxford

```

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