Re: NullSpace[m], why different result for symbolic vs numerical matrix?
- To: mathgroup at smc.vnet.net
- Subject: [mg59261] Re: NullSpace[m], why different result for symbolic vs numerical matrix?
- From: Bill Rowe <readnewsciv at earthlink.net>
- Date: Wed, 3 Aug 2005 01:20:02 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On 8/2/05 at 12:42 AM, nma at 12000.org (Nasser Abbasi) wrote:
>hello, This 5.2 on windows.
>The help for NullSpace function says:
>"NullSpace works on both numerical and symbolic matrices. "
>But why do I get different answer if matrix A is numeric vs
>symbolic?
>What Am I missing?
>Both answers are correct in the sense that A times each of null
>vectors produced does give 0.
>------------
> Remove["Global`*"]
>A = {{0, 1, 1, 2}, {1, 2, 3, 4}, {2, 0, 2, 0}};
>m1 = NullSpace[A]
>m2 = NullSpace[N[A, 16]]
Both examples above are numerical not symbolic. One example uses exact arithmetic and the other uses a specified precision. It should never be surprising when an exact answer differs from an answer using lower precision arithmetic. That is the nature of using low precision arithmetic.
Also, there is no unique solution to the problem since for any matrix A and vector x if A.x = 0 then A.y = 0 when y = k x for any arbitrary constant k.
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