Analytical expression for the eigenvectors of a 3x3 real, symmetric matrix? I am writing an algorithm that process 3D images based on the local moment of inertia. 

I have a 3x3 real symmetric matrix, from which I need to find the eigenvalues. I have found a variety of generic algorithm for the diagonalization of matrices out there, but I could not get to know if there exists an analytical expression for the 3 eigenvctors of such a matrix. 

Would someone proficient in maths know that? 



EDIT

For the record here is what I have found on the question myself.
As Matthias Odisio said, you can't get down to a simple analytical expression as soon as you have a 3x3 matrix. 

I have found however a dedicated paper for the special case a 3x3 hermitian matrices, where various numerical specialized approaches are compared:

http://arxiv.org/abs/physics/0610206

Here is the C and Fortran code of the paper:

http://www.mpi-hd.mpg.de/personalhomes/globes/3x3/index.html
Wolfram|Alpha has made such things easy: