Re: Determining Linear dependent vectors

*To*: mathgroup at smc.vnet.net*Subject*: [mg66272] Re: [mg66248] Determining Linear dependent vectors*From*: "David Park" <djmp at earthlink.net>*Date*: Sat, 6 May 2006 01:55:07 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Here is a set of vectors in the rows. vectors = {{1, 0, 3, 2, 0}, {0, 1, 2, 0, 3}, {1, 1, 5, 2, 3}, {2, -1, 4, 4, -3}, {1, 2, 7, 2, 6}}; Here is the null space of the transpose of vectors. nmat = NullSpace[Transpose@vectors] {{-1, -2, 0, 0, 1}, {-2, 1, 0, 1, 0}, {-1, -1, 1, 0, 0}} Multiplying the null space vectors times vectors gives all zeros. nmat.vectors {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}} We have three dependent vectors and we can solve for them in terms of the first two independent vectors. Label the vectors {v1,v2,v3,v4,v5}. Then Thread[nmat.{v1, v2, v3, v4, v5} == {0, 0, 0}] Solve[%, {v3, v4, v5}] {-v1 - 2 v2 + v5 == 0, -2 v1 + v2 + v4 == 0, -v1 - v2 + v3 == 0} {{v5 -> v1 + 2 v2, v4 -> 2 v1 - v2, v3 -> v1 + v2}} David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Saurabh [mailto:saurabh911 at gmail.com] To: mathgroup at smc.vnet.net Am looking for methods to determine linearly dependent vectors out of a given set. Any pointers appreciated. Thanks,

**Follow-Ups**:**Re: Re: Determining Linear dependent vectors***From:*pratikd@wolfram.com