Re: nullspaces

• To: mathgroup at smc.vnet.net
• Subject: [mg68988] Re: [mg68948] nullspaces
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Sat, 26 Aug 2006 02:04:24 -0400 (EDT)
• References: <200608250934.FAA09201@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On Aug 25, 2006, at 5:34 AM, hespeler wrote:

> Hello
>
> I have a general problem with the computation of nullspaces for
> large dense matrices, e.g. dim(2,108), explicit example is added at
> the end of the mail. Using the internal command B=NullSpace[A] (A
> is an inexact, potentially complex matrix) and trying to reconfirm
> the result by
>
> Chop[A.ConjugateTranspose[NullSpace[B]]]==N[ZeroMatrix[Dimensions[A]
> [[1]],Dimensions[B][[1]]]]

The way NullSpace is defined the correct check is Chop[A.Transpose[B]]
==ZeroMatrix[First[Dimensions[A]],First[Dimensions[B]]] there is no
need to take conjugates or to apply NullSpace again.

for example:

In[122]:=
Block[{a=Table[Random[Complex,{-1-I,1+I}],{2},{108}],b},b=NullSpace[a];
Chop[a.Transpose[b]]==ZeroMatrix[First[Dimensions[a]],First
[Dimensions[b]]]]
Out[122]=
True

Regards,

Ssezi

```

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