Re: RE: RE: Generating Two Unit Orthogonal Vectors
- To: mathgroup at smc.vnet.net
- Subject: [mg36493] Re: [mg36476] RE: [mg36448] RE: Generating Two Unit Orthogonal Vectors
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Mon, 9 Sep 2002 00:29:35 -0400 (EDT)
- References: <200209080731.DAA05434@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
> Wouldn't it be nice if NullSpace's behavior were DOCUMENTED? Otherwise,
> it's futile to give it approximate numbers expecting any particular
> behavior. Even if it always works, it may not work in the next version
> of Mathematica.
The expected, and documented, behavior is that the output should be a
basis for the null space, that is, solutions of the homogeneous matrix
equation A.x==0. If this were to stop working then that would be a
serious bug. Is this the behavior you mean?
The implementation notes of the manual mention that approximate
NullSpace is based on a singular values decomposition. This in fact
gives resulting vectors that are orthonormal by the usual
conjugate-symmetric inner product on C (though these are now not
"normal" to the original vector in this same inner product, unless they
are real-valued). But this basis-orthogonality is not part of the
mission of NullSpace and moreover should not become part of it. Hence
that particular (and implementation dependent) aspect of NullSpace
should not become documented.
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