Representation of a Rotation Matrix

[Dahaka14]

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:

$$\left(\begin{array}{ccc} A & B & C \\ B & D & E \\ C & E & D \end{array}\right)$$ ,

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.

 

[fresh_42]

A symmetric matrix can be diagonalized by orthogonal matrices. I suggest to perform this algorithm.