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?
Most efficient way to compute eigenvectors / values of this matrix?
linear algebra;eigenvalues