Varimax Rotation Properties

I have written a varimax rotation in C++ and run it on
the "Five Socio-Economic Variables" used in Harman,
third edition. All computation are in C++ double
(64 bit floating point). Here are my results:

rotated factor coefficients: 5 2
-0.993765 0.016025
0.008817 0.940759
-0.980067 0.137021
-0.447137 0.824806
0.006050 0.968227

These results agree with Harman (Table 13.6) with an
error no greater than +- 0.00003 (not good enough if
you ask me) notwithstanding some difference in
arrangement.

Next I multiplied this matrix by the original data,
to get a 12x2 matrix and computed the unbiased
Pearson correlation matrix on the columns. Here
are the results:

cor: 2 2
1.000000 -0.090594
-0.090594 1.000000

I would have expected the off-diagonal correlations
to be essentially zero, which they clearly are not.

Wherein to I err?

Thanks for your help.
Mike.

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