Re: LU Decompsoition for singular matrices

• To: mathgroup at smc.vnet.net
• Subject: [mg33271] Re: LU Decompsoition for singular matrices
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 13 Mar 2002 03:14:38 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <a6kko6\$d3p\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

what may the SingularValue[] function do ?

"SingularValues[m] gives the singular value decomposition for a
numerical \
matrix m. The result is a list {u, w, v}, where w is the list of
singular \
values, and m can be written as
Conjugate[Transpose[u]].DiagonalMatrix[w].v"

Regards
Jens

>
> 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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