GramSchmidt Orthogonalization question

*To*: mathgroup at smc.vnet.net*Subject*: [mg14291] GramSchmidt Orthogonalization question*From*: Steve Reagan <swr4f at virginia.edu>*Date*: Tue, 13 Oct 1998 01:21:11 -0400*Organization*: University of Virginia*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: GramSchmidt Orthogonalization question***From:*Jurgen Tischer <jtischer@col2.telecom.com.co>