[R] SVD and spectral decompositions of a hermitian matrix

[Ravi Varadhan]

Hi:

I create a hermitian matrix and then perform its singular value 
decomposition. But when I put it back, I don't get the original 
hermitian matrix.  I am having the same problem with spectral value 
decomposition as well.

I am using R 1.7.0 on Windows.  Here is my code:

X <- matrix(rnorm(16)+1i*rnorm(16),4)
X <- X + t(X)
X[upper.tri(X)] <- Conj(X[upper.tri(X)])
Y <- La.svd(X)
Y$u %*% diag(Y$d) %*% t(Y$v)   # this doesn't give back X
Y$u %*% diag(Y$d) %*% Y$v      # this works fine.
Z <- La.eigen(X)   # the eigen values should be real, but are not.
Z$vec %*% diag(Z$val) %*% t(Z$vec)   # this doesn't give back X

The help for "La.svd" says that the function return U, D, and V such 
that X = U D V'  Furthermore, the help for "La.eigen" says that if the 
argument "symmetric" is not specified, the matrix is inspected for 
symmetry, so I expect that I should get real eigen values to a 
hermitian matrix. Are there any problems with these 2 functions, or 
what is it that I am not understanding? 

thanks for your help,
Ravi.