Dear Peng, This seems a curious question to pose on r-help: The vector 1 is the first column of X, and hence lies in the subspace spanned by the columns of X. H projects any vector orthogonally onto the subspace spanned by X. Thus, if a vector, such as 1, lies in this subspace, it's projected onto itself.
Regards, John > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On > Behalf Of Peng Yu > Sent: October-11-09 2:03 PM > To: r-h...@stat.math.ethz.ch > Subject: [R] Why H1=1? (H's the hat matrix) > > Suppose I have the following hat matrix: > > H=X(X'X)^{-1}X' > X is a n by p matrix, where n >= p and X_{i,1} = 1 > > I'm wondering why H1 = 1. (Here, 1 is column vector, whose each > element is the number 1) > > Thank you! > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.