Re: GramSchmidt Orthogonalization question

• To: mathgroup at smc.vnet.net
• Subject: [mg14333] Re: [mg14291] GramSchmidt Orthogonalization question
• From: "Jens-Peer Kuska" <kuska at linmpi.mpg.de>
• Date: Thu, 15 Oct 1998 00:28:39 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Steve,

as far as I see the set of eigenvectors is produced correctly. If You
don't like the error messages You can simply trun it of by
Off[Power::infy]
Off[indet::Indeterminate]
Off[Power::infy]
Off[indet::Indeterminate]

Hope that helps
Jens
-----Original Message-----
From: Steve Reagan <swr4f at virginia.edu> To: mathgroup at smc.vnet.net
Subject: [mg14333] [mg14291] GramSchmidt Orthogonalization question

>The LinearAlgebra'Orthogonalization' package seems to have a problem
>when dealing with a set of dependent vectors:
>
><<LinearAlgebra`Orthogonalization`
>v1={3+2I,3-2I,5};
>v2={3-2I,3+2I,5};
>v3={5,7,-12};
>v4=2*v1;
>v5=-7*v3;
>GramSchmidt[{v1,v2,v3,v4},Normalized->False]
>
>{{3 + 2*I, 3 - 2*I, 5},
>{-48/35 - (172*I)/35, -48/35 + (172*I)/35, -16/7}, {330/43, 330/43,
>-396/43},
>{0, 0, 0}}
>
>GramSchmidt[{v1,v2,v3,v4,v5},Normalized->False] Power::infy  Infinite
>expression 1/0 encountered. indet:Indeterminate expression
>0*ComplexInfinity encountered.
>
>{{3 + 2*I, 3 - 2*I, 5}, {-48/35 - (172*I)/35, -48/35 + (172*I)/35,
>-16/7}, {330/43, 330/43, -396/43},
>  {0, 0, 0}, {Indeterminate, Indeterminate, Indeterminate}}
>
>When the number of vectors in the input list exceeds the number of
>independent ones by exactly one, there is no problem as shown in first
>example.  But, if a larger list is used for input, errors result as
>shown in the second example.
>
>Is there an extension or package that handles dependent sets such that
>an orthogonal set is produced correctly ?
>