SVD/Eigenvector confusion

Is there a reason you are doing the SVD in such a complicated way?
Why not use the svd function directly?

I am using it to debug other code that is deigned to compute SVDs, so I 
actually want to understand the intermediate steps in constricting the SVD.

Nothing I have seen in the various books & net sources I have read seem to 
indicate that the eigenvectors for U & V have any special requirements 
other than being of unit length, but the experimentation in R seems to 
indicate otherwise, hence my confusion.

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