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?
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:
Here is the C and Fortran code of the paper: