R help - Mar 2013 - Same eigenvalues but different eigenvectors using 'prcomp' and 'principal' commands

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]]

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]]
>