Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

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,


  • Prev by Date: Re: Evaluating integrals
  • Next by Date: Re: Determining Linear dependent vectors
  • Previous by thread: Re: Determining Linear dependent vectors
  • Next by thread: Re: Determining Linear dependent vectors