correlation question

TEMPL Matthias a ??crit :

First: The question is really not related to R.
What you can find very easly in books or in the internet:
The correlation coefficient is invariant under a linear transformation
(and the proof) 

yes.

#E.g. 
library(rrcov)
data(brain)
cor(brain)
cor(scale(brain))  #Is the same,

ok

cor(log(brain))    # BUT Is VERY different.

Ah, thank you very much for this example.
So it seems cor(X,Y) ~ cor(log(X), log(Y)) is in fact
only a particular feature of my data (prices series)
(perhaps/probably because they are quite continuous ?).

Nothing general. I was completely off the track. Sorry.

Best,
Matthias

Thanks again for this counter-example and the enlightenment.
Vincent