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

DrBob wrote: > > 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. > > Bobby 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. Daniel Lichtblau Wolfram Research

**References**:**RE: RE: Generating Two Unit Orthogonal Vectors***From:*"DrBob" <drbob@bigfoot.com>