spectral-decomposition

I have the following problem:

I try to make the spectral decomposition
for the following matrix by utilising the
function eigen.

 0.4015427  0.08903581 -0.2304132
 0.08903581 1.60844812  0.9061157
-0.23041322 0.9061157   2.9692562

When checking the result I was not able
to produce the original matrix by using
the decomposition. It also appears that
the product T'T, where T is a matrix of
eigenvectors, is not an identity matrix.

 Tapio Nummi
 University of Tampere

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