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  \code{\link{capabilities}} to test for IEEE 754 arithmetic.
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  \code{\link{capabilities}} to test for IEEE 754 arithmetic.
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}
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}
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\examples{
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\examples{
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hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
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hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
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str(X <- hilbert(9)[,1:6])
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X <- hilbert(9)[,1:6]
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str(s <- svd(X))
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(s <- svd(X))
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D <- diag(s$d)
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D <- diag(s$d)
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s$u \%*\% D \%*\% t(s$v) #  X = U D V'
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s$u \%*\% D \%*\% t(s$v) #  X = U D V'
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t(s$u) \%*\% X \%*\% s$v #  D = U' X V
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t(s$u) \%*\% X \%*\% s$v #  D = U' X V
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}
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}
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\keyword{algebra}
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\keyword{algebra}