I have a symmetric $ 3 \times 3 $ matrix $A$ and I need to compute the eigenvectors and eigenvalues of this. I know that I can use something like Lapack, but I also know that this can be computed analytically.
The physics suggest that this will have only real eigenvalues, but the analytic expression allows for imaginary numbers.
- Is there a simply analytic expression for this?
- If I can generate the characteristic equation analytically, would it be most efficient to solve this equation numerically to obtain the eigenvalues?
- Is it just as simple / efficient to simply use something like Lapack for this?
- Any other ideas?