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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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