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Same eigenvalues but different eigenvectors using 'prcomp' and 'principal' commands
3 messages · Arlindo Meque, Ben Bolker, John Fox
Arlindo Meque <mequitomz <at> yahoo.com.br> writes:
Dear all, I've used the 'prcomp' command to calculate the eigenvalues and eigenvectors of a matrix(gg). Using the command 'principal' from the 'psych' package? I've performed the same exercise. I got the same eigenvalues but different eigenvectors. Is there any reason for that difference?
[snip] eigenvectors are only defined up to a scale factor. prcomp is scaling them so that the sum of squares is 1; I haven't bothered to see how principal() is scaling them (maybe the documention says). (1,1) and (-1,1) , or (1,1) and (1,-1), would have been equally valid choices. Ben Bolker
Dear Arlindo, When, as here, the eigenvalues are distinct, corresponding eigenvectors are defined only up to multiplication by a nonzero constant. As you can verify, the first set of eigevectors is normalized to length 1 while the second set is normalized to have length equal to the corresponding eigenvalues. I hope this helps, John ------------------------------------------------ John Fox Sen. William McMaster Prof. of Social Statistics Department of Sociology McMaster University Hamilton, Ontario, Canada http://socserv.mcmaster.ca/jfox/ On Thu, 14 Mar 2013 01:01:56 -0700 (PDT)
Arlindo Meque <mequitomz at yahoo.com.br> wrote:
Dear all, I've used the 'prcomp' command to calculate the eigenvalues and eigenvectors of a matrix(gg). Using the command 'principal' from the 'psych' package? I've performed the same exercise. I got the same eigenvalues but different eigenvectors. Is there any reason for that difference? Below are the steps I've followed: 1. PRCOMP #defining the matrix gg=matrix(byrow = TRUE, nrow = 3,data = c(1, 0, 1, 1, 4, 2))
gg
[,1] [,2] [1,] 1 0 [2,] 1 1 [3,] 4 2 pc=prcomp(gg,center=TRUE,scale=TRUE) # The eigenvectors pc$rotation PC1 PC2 [1,] 0.7071068 0.7071068 [2,] 0.7071068 -0.7071068 # The eigenvalues:
pc$sdev^2
[1] 1.8660254 0.1339746 2. PSYCH Package:
pp=principal(gg,nfactors=2)
# The eigenvectors
pp$loadings
Loadings: PC1 PC2 [1,] 0.966 -0.259 [2,] 0.966 0.259 # The eigenvalues pp$values 1] 1.8660254 0.1339746 Sincerely, Arlindo [[alternative HTML version deleted]]