For summary(GAM) in the mgcv package smooth the degrees of freedom for
the F value for test of smooth terms are the rank of covariance matrix
of \hat{beta} and the residuals df.  I've noticed that in a lot of GAMs
I've fit the rank of the covariance turns out to be 9.  In Simon Wood's
book, the rank of covariance matrix is usually either 9 or 99 (pages
239-230 and 259).  
 
Can anyone comment on why so many smooth terms have a denominator
degree of freedom involving 9.  Simon Wood writes "r is usually
determinted numerically, while forming the pseudoinverse of the
covariance matrix, or with reference to the effective degrees of freedom
of the term" which doesn't really clarify the issue for me at least.
 
Thanks.
 
Brendan Klick
Johns Hopkins University School of Medicine.

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