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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:

[tex] \left(\begin{array}{ccc}

A & B & C \\

B & D & E \\

C & E & D

\end{array}\right) [/tex] ,

with A, B, C, D, and E all involving somewhat simple terms with sines and cosines of up to 3 angles (i.e. [tex] \sin\theta 12[/tex], [tex]\cos\theta 13[/tex], and [tex]\sin\theta 23 [/tex]). 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.

[tex] \left(\begin{array}{ccc}

A & B & C \\

B & D & E \\

C & E & D

\end{array}\right) [/tex] ,

with A, B, C, D, and E all involving somewhat simple terms with sines and cosines of up to 3 angles (i.e. [tex] \sin\theta 12[/tex], [tex]\cos\theta 13[/tex], and [tex]\sin\theta 23 [/tex]). 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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