Re: Determining Linear dependent vectors

*To*: mathgroup at smc.vnet.net*Subject*: [mg66259] Re: Determining Linear dependent vectors*From*: "ben" <benjamin.friedrich at gmail.com>*Date*: Sat, 6 May 2006 01:54:29 -0400 (EDT)*References*: <e3f5s6$sac$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Saurabh The easiest way is to apply Gram-Schmidt, though no need to normalize your vectors. To account for round-off errors, maybe replace != by sth. like "norm<2 machine precison". The following code tells you which vectors to keep, in order to get a linearly independent set. All vectors M[[m]] that end up as {0,0,0} are linearly dependent from all M[[n]], n<m with M[[m]].M[[n]] != 0. Bye Ben (* some vectors *) M = Table[Random[Integer], {i, 10}, {j, 3}] (* Gram - Schmidt *) Do[ Do[If[M[[n]] != {0, 0, 0}, M[[m]] = (M[[n]].M[[n]]) M[[m]] - (M[[n]].M[[m]])M[[n]]], {n, 1, m - 1}], {m, 2, 10}] (* result *) Map[If[# != {0, 0, 0}, "keep", "discard"] &, M] Saurabh schrieb: > Am looking for methods to determine linearly dependent vectors out of a given set. Any pointers appreciated. > > Thanks,