[R] B %*% t(B) = R , then solve for B

From: Shawn Koppenhoefer <shawn.koppenhoefer_at_epfl.ch>
Date: Tue, 12 Apr 2011 14:39:05 +0200


Hello,..
Apologies for the newbie question but...

I have a matrix R, and I know that *B %*% t(b) = R* *I'm trying to solve for B *(aka. 'factoring the correlation matrix' I think)
Please help!

I've read that 'to solve for B we define the eigenvalues of R and then apply the techniques of Principal Component Analysis' This made me reach for princomp() but now I'm stuck.

I think to understand, that I should be doing this:

       pc<-princomp(covmat=R, cor=TRUE)

This gives me :

     Standard deviations:
     Comp.1   Comp.2   Comp.3
     1.208492 1.076105 0.617694

But what do I do with that, in order to construct B ??

Thanks for any help anyone can give,... even if it's just a pointer to an example... free beer to anyone who can save me.

/Shawn

p.s. I read/understand Thursstone_1944 which gives a graphical method of Factoring the Correlation Matrix, which I understand... but surely R provides me a way of determining B? And I know that the answer is encrypted in Harman_1960.

p.p.s. Here's my R (in case you're curious and want to help):

R<-matrix(c(0.6099, 0.2558, 0.1858,

             0.2558,  0.5127,  -.1384,
             0.1858, -0.1384,   0.9351 ),
           nrow=3, ncol=3, byrow=TRUE)


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