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] (* Your code ...*) 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 ? > >Thank you in advance, >Steve Reagan > > >