Representation of a Rotation Matrix

Dahaka14
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Say I have a matrix similar to the SO(3) matrix for general 3-D rotations, except it has slightly different (simpler) elements, and the symmetry is as follows:

\left(\begin{array}{ccc}<br /> A &amp; B &amp; C \\<br /> B &amp; D &amp; E \\<br /> C &amp; E &amp; D<br /> \end{array}\right) ,

with A, B, C, D, and E all involving somewhat simple terms with sines and cosines of up to 3 angles (i.e. \sin\theta 12, \cos\theta 13, and \sin\theta 23). Is it possible to put this matrix into a basis using only 3 independent unit vector matrices? Let me know if you want more info.
 
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A symmetric matrix can be diagonalized by orthogonal matrices. I suggest to perform this algorithm.
 

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