x <- matrix(rnorm(1:20), 5, 4)
x.qr <- qr(x)

Q <- qr.Q(x.qr)
R <- qr.R(x.qr)
X <- qr.X(x.qr)

Q
R
X
Q %*% R

qr.Q(x.qr, complete=TRUE)  ## orthogonal completion

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