Eigenvectors are unique only up to a constant factor, so any scalar multiple of an eigenvector is also an eigenvector. By convention, most (all) packages normalize the eigenvectors such that their norm is 1. Therefore, eigenvectors are unique up to their sign, i.e. if (+x) is an eigenvector corresponding to an eigenvalue, then (-x) is also an eigenvector for the same eigenvalue.
Hope this helps, Ravi. -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of rkevinbur...@charter.net Sent: Wednesday, June 23, 2010 6:32 PM To: r-help@r-project.org Subject: [R] Beginning Eigen System question. Forgive me if I missunderstand a basic Eigensystem but when I present the following matrix to most any other LinearAlgebra system: 1 3 1 1 2 2 1 1 3 I get an answer like: //$values //[1] 5.000000e+00 1.000000e+00 -5.536207e-16 //$vectors // [,1] [,2] [,3] //[1,] 0.5773503 -0.8451543 -0.9428090 //[2,] 0.5773503 -0.1690309 0.2357023 //[3,] 0.5773503 0.5070926 0.2357023 But R gives me: //$values //[1] 5.000000e+00 1.000000e+00 -5.536207e-16 //$vectors // [,1] [,2] [,3] //[1,] -0.5773503 -0.8451543 -0.9428090 //[2,] -0.5773503 -0.1690309 0.2357023 //[3,] -0.5773503 0.5070926 0.2357023 The only difference seems to be the sign on the first eigen vector. What am I missing? Kevin ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
